Electrical Engineering

#16: Post edited by

Andy aka‭ · 2022-05-04T11:04:50Z (almost 2 years ago)

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~~"React" implies a response to an event. The event is a change in current, \$\frac{di}{dt}\$ for an inductor and, for a capacitor, the event is a change in voltage, \$\frac{dv}{dt}\$.~~
$$$$
So, an inductor or capacitor will produce a proportional reaction (or response) to something changing. If we say that a capacitor **responds** to a change in voltage, we then have to define that **response** and, the only thing it **can do** is alter its current. Therefore we can say that the transfer function of a capacitor is: its response current (\$i\$) divided by its input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\cdot\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\cdot\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

"React" implies a response to an "event".
- For an inductor, the "event" is a change in current, \$\frac{di}{dt}\$
- For a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$
$$$$
So, an inductor or capacitor will produce a proportional reaction (or response) to something changing. If we say that a capacitor **responds** to a change in voltage, we then have to define that **response** and, the only thing it **can do** is alter its current. Therefore we can say that the transfer function of a capacitor is: its response current (\$i\$) divided by its input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\cdot\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\cdot\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

#15: Post edited by

Andy aka‭ · 2022-05-03T12:10:30Z (almost 2 years ago)

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"React" implies a response to an event. The event is a change in current, \$\frac{di}{dt}\$ for an inductor and, for a capacitor, the event is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
So, an inductor or capacitor will produce a rate-proportional reaction (or response) to something changing. If we say that a capacitor **responds** to a change in voltage, we then have to define that **response** and, the only thing it **can do** is alter its current. Therefore we can say that the transfer function of a capacitor is: its response current (\$i\$) divided by its input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\cdot\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\cdot\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

"React" implies a response to an event. The event is a change in current, \$\frac{di}{dt}\$ for an inductor and, for a capacitor, the event is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
So, an inductor or capacitor will produce a proportional reaction (or response) to something changing. If we say that a capacitor **responds** to a change in voltage, we then have to define that **response** and, the only thing it **can do** is alter its current. Therefore we can say that the transfer function of a capacitor is: its response current (\$i\$) divided by its input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\cdot\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\cdot\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

#14: Post edited by

Andy aka‭ · 2022-05-03T12:09:56Z (almost 2 years ago)

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The word "react" implies that something responds to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
~~So, an inductor or capacitor will produce a proportional reaction (or response) to something changing at a fixed rate.~~
~~$$$$~~
If we say that a capacitor **responds** to a change in voltage, we then have to define that **response** and, the only thing it **can do** is alter its current. Therefore we can say that the transfer function of a capacitor is: its response current (\$i\$) divided by its input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\cdot\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\cdot\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

"React" implies a response to an event. The event is a change in current, \$\frac{di}{dt}\$ for an inductor and, for a capacitor, the event is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
So, an inductor or capacitor will produce a rate-proportional reaction (or response) to something changing. If we say that a capacitor **responds** to a change in voltage, we then have to define that **response** and, the only thing it **can do** is alter its current. Therefore we can say that the transfer function of a capacitor is: its response current (\$i\$) divided by its input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\cdot\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\cdot\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

#13: Post edited by

Andy aka‭ · 2022-04-24T18:52:10Z (almost 2 years ago)

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The word "react" implies that something responds to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
~~An inductor or capacitor produces a proportional reaction to something changing at a fixed rate.~~
$$$$
If we say that a capacitor **responds** to a change in voltage, we then have to define that **response** and, the only thing it **can do** is alter its current. Therefore we can say that the transfer function of a capacitor is: its response current (\$i\$) divided by its input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\cdot\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\cdot\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

The word "react" implies that something responds to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
So, an inductor or capacitor will produce a proportional reaction (or response) to something changing at a fixed rate.
$$$$
If we say that a capacitor **responds** to a change in voltage, we then have to define that **response** and, the only thing it **can do** is alter its current. Therefore we can say that the transfer function of a capacitor is: its response current (\$i\$) divided by its input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\cdot\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\cdot\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

#12: Post edited by

Andy aka‭ · 2022-04-24T18:50:27Z (almost 2 years ago)

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The word "react" implies that something responds to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
The inductor or capacitor produces a fixed reaction to something that changes at a fixed rate.
$$$$
So, if we say that the output of a capacitor is **a reaction** to a change in voltage, we then have to state how it reacts and, the only thing it **can do** is alter the current flow. Therefore we can say that the transfer function of a capacitor is: its output current (\$i\$) over its input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\cdot\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\cdot\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

The word "react" implies that something responds to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
An inductor or capacitor produces a proportional reaction to something changing at a fixed rate.
$$$$
If we say that a capacitor **responds** to a change in voltage, we then have to define that **response** and, the only thing it **can do** is alter its current. Therefore we can say that the transfer function of a capacitor is: its response current (\$i\$) divided by its input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\cdot\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\cdot\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

#11: Post edited by

Andy aka‭ · 2022-04-24T15:10:27Z (almost 2 years ago)

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The word "react" implies that something responds to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
~~The inductor or capacitor produces a fixed reaction to something that is changing at a fixed rate.~~
$$$$
So, if we say that the output of a capacitor is **a reaction** to a change in voltage, we then have to state how it reacts and, the only thing it **can do** is alter the current flow. Therefore we can say that the transfer function of a capacitor is: its output current (\$i\$) over its input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\cdot\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\cdot\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

The word "react" implies that something responds to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
The inductor or capacitor produces a fixed reaction to something that changes at a fixed rate.
$$$$
So, if we say that the output of a capacitor is **a reaction** to a change in voltage, we then have to state how it reacts and, the only thing it **can do** is alter the current flow. Therefore we can say that the transfer function of a capacitor is: its output current (\$i\$) over its input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\cdot\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\cdot\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

#10: Post edited by

Andy aka‭ · 2022-04-24T15:08:29Z (almost 2 years ago)

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The word "react" implies that something responds to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
And, of course you can't define a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is producing a fixed reaction to something that is changing at a fixed rate.
$$$$
So, if we say that the output of a capacitor is **a reaction** to a change in voltage, we then have to state how it reacts and, the only thing it **can do** is alter the current flow. Therefore we can say that the transfer function of a capacitor is: its output current (\$i\$) over its input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\cdot\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\cdot\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

The word "react" implies that something responds to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
The inductor or capacitor produces a fixed reaction to something that is changing at a fixed rate.
$$$$
So, if we say that the output of a capacitor is **a reaction** to a change in voltage, we then have to state how it reacts and, the only thing it **can do** is alter the current flow. Therefore we can say that the transfer function of a capacitor is: its output current (\$i\$) over its input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\cdot\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\cdot\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

#9: Post edited by

Andy aka‭ · 2022-04-24T15:06:53Z (almost 2 years ago)

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The word "react" implies that something responds to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
~~And, of course you can't define a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing.~~
$$$$
So, if we say that the output of a capacitor is **a reaction** to a change in voltage, we then have to state how it reacts and, the only thing it **can do** is alter the current flow. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\cdot\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\cdot\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

The word "react" implies that something responds to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
And, of course you can't define a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is producing a fixed reaction to something that is changing at a fixed rate.
$$$$
So, if we say that the output of a capacitor is **a reaction** to a change in voltage, we then have to state how it reacts and, the only thing it **can do** is alter the current flow. Therefore we can say that the transfer function of a capacitor is: its output current (\$i\$) over its input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\cdot\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\cdot\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

#8: Post edited by

Andy aka‭ · 2022-04-23T17:01:34Z (about 2 years ago)

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The word "react" implies that something responds to an event change. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
And, of course you can't define a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing.
$$$$
So, if we say that the output of a capacitor is **a reaction** to a change in voltage, we then have to state how it reacts and, the only thing it **can do** is alter the current flow. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\cdot\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\cdot\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

The word "react" implies that something responds to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
And, of course you can't define a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing.
$$$$
So, if we say that the output of a capacitor is **a reaction** to a change in voltage, we then have to state how it reacts and, the only thing it **can do** is alter the current flow. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\cdot\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\cdot\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

#7: Post edited by

Andy aka‭ · 2022-04-23T09:06:39Z (about 2 years ago)

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The word "react" implies that something responds to an event change. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
~~And, of course you can't measure a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing; there is a _"reactance"_.~~
$$$$
So, if we say that the output of a capacitor is **a reactance** to a change in voltage we then have to state how it reacts and, the only thing it **can do** is alter current. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\cdot\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\cdot\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

The word "react" implies that something responds to an event change. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
And, of course you can't define a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing.
$$$$
So, if we say that the output of a capacitor is **a reaction** to a change in voltage, we then have to state how it reacts and, the only thing it **can do** is alter the current flow. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\cdot\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\cdot\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

#6: Post edited by

Andy aka‭ · 2022-04-23T08:54:44Z (about 2 years ago)

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"Reactance" is a word that is similar to "resistance" but, it's not the same; there is a subtle difference. The word "react" implies that something "reacts" to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
And, of course you can't measure a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing; there is a _"reactance"_.
$$$$
So, if we say that the output of a capacitor is **a reactance** to a change in voltage we then have to state how it reacts and, the only thing it **can do** is alter current. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\cdot\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\cdot\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

The word "react" implies that something responds to an event change. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
And, of course you can't measure a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing; there is a _"reactance"_.
$$$$
So, if we say that the output of a capacitor is **a reactance** to a change in voltage we then have to state how it reacts and, the only thing it **can do** is alter current. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\cdot\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\cdot\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

#5: Post edited by

Andy aka‭ · 2022-04-22T18:24:36Z (about 2 years ago)

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"Reactance" is a word that is similar to "resistance" but, it's not the same; there is a subtle difference. The word "react" implies that something "reacts" to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
And, of course you can't measure a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing; there is a _"reactance"_.
$$$$
So, if we say that the output of a capacitor is **a reactance** to a change in voltage we then have to state how it reacts and, the only thing it **can do** is alter current. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
~~$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$~~
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
~~$$v = L\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$~~

"Reactance" is a word that is similar to "resistance" but, it's not the same; there is a subtle difference. The word "react" implies that something "reacts" to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
And, of course you can't measure a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing; there is a _"reactance"_.
$$$$
So, if we say that the output of a capacitor is **a reactance** to a change in voltage we then have to state how it reacts and, the only thing it **can do** is alter current. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\cdot\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\cdot\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

#4: Post edited by

Andy aka‭ · 2022-04-22T18:23:54Z (about 2 years ago)

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"Reactance" is a word that is similar to "resistance" but, it's not the same; there is a subtle difference. The word "react" implies that something "reacts" to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
And, of course you can't measure a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing; there is a _"reactance"_.
$$$$
So, if we say that the output of a capacitor is **a reactance** to a change in voltage we then have to state how it reacts and, the only thing it **can do** is alter current. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
~~$$v = L\dfrac{di}{dt}$$~~

"Reactance" is a word that is similar to "resistance" but, it's not the same; there is a subtle difference. The word "react" implies that something "reacts" to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
And, of course you can't measure a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing; there is a _"reactance"_.
$$$$
So, if we say that the output of a capacitor is **a reactance** to a change in voltage we then have to state how it reacts and, the only thing it **can do** is alter current. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\dfrac{di}{dt}\hspace{1cm} \text{ the standard inductance formula}$$

#3: Post edited by

Andy aka‭ · 2022-04-22T18:22:56Z (about 2 years ago)

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"Reactance" is a word that is similar to "resistance" but, it's not the same; there is a subtle difference. The word "react" implies that something "reacts" to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
~~And, of course you can't measure a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing.~~
$$$$
So, if we say that the output of a capacitor is **a reactance** to a change in voltage we then have to state how it reacts and, the only thing it **can do** is alter current. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -
~~$$\dfrac{i}{\frac{dv}{dt}}$$~~
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
~~$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\dfrac{dv}{dt}$$~~
~~For an inductor, the reactive output is voltage and, if we went through the same procedure as we did (above) for a capacitor we would find that: -~~
$$v = L\dfrac{di}{dt}$$

"Reactance" is a word that is similar to "resistance" but, it's not the same; there is a subtle difference. The word "react" implies that something "reacts" to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
And, of course you can't measure a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing; there is a _"reactance"_.
$$$$
So, if we say that the output of a capacitor is **a reactance** to a change in voltage we then have to state how it reacts and, the only thing it **can do** is alter current. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}} = \dfrac{\text{A current is produced}}{\text{For a change in voltage}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\dfrac{dv}{dt}\hspace{1cm} \text{ the standard capacitance formula}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did for a capacitor, we would find that: -
$$v = L\dfrac{di}{dt}$$

#2: Post edited by

Andy aka‭ · 2022-04-22T18:01:45Z (about 2 years ago)

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"Reactance" is a word that is similar to "resistance" but, it's not the same; there is a subtloe difference. The word "react" implies that something "reacts" to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
And, of course you can't measure a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing.
$$$$
So, if we say that the output of a capacitor is **a reactance** to a change in voltage we then have to state how it reacts and, the only thing it **can do** is alter current. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\dfrac{dv}{dt}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did (above) for a capacitor we would find that: -
$$v = L\dfrac{di}{dt}$$

"Reactance" is a word that is similar to "resistance" but, it's not the same; there is a subtle difference. The word "react" implies that something "reacts" to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
And, of course you can't measure a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing.
$$$$
So, if we say that the output of a capacitor is **a reactance** to a change in voltage we then have to state how it reacts and, the only thing it **can do** is alter current. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -
$$\dfrac{i}{\frac{dv}{dt}}$$
And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -
$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\dfrac{dv}{dt}$$
For an inductor, the reactive output is voltage and, if we went through the same procedure as we did (above) for a capacitor we would find that: -
$$v = L\dfrac{di}{dt}$$

#1: Initial revision by

Andy aka‭ · 2022-04-22T18:00:22Z (about 2 years ago)

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"Reactance" is a word that is similar to "resistance" but, it's not the same; there is a subtloe difference. The word "react" implies that something "reacts" to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
$$$$
And, of course you can't measure a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing. 
$$$$
So, if we say that the output of a capacitor is **a reactance** to a change in voltage we then have to state how it reacts and, the only thing it **can do** is alter current. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -

$$\dfrac{i}{\frac{dv}{dt}}$$

And we call that transfer function, (unsurprisingly) capacitance. Rearranging we get this: -

$$C = \dfrac{i}{\frac{dv}{dt}}\hspace{1cm} \text{ or}\hspace{1cm} i = C\dfrac{dv}{dt}$$

For an inductor, the reactive output is voltage and, if we went through the same procedure as we did (above) for a capacitor we would find that: -

$$v = L\dfrac{di}{dt}$$

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