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"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, $\frac{dv}{dt}$ $$$$ So, ...
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#16: Post edited
"React" implies a response to an event. The event is a change in current, \$\frac{di}{dt}\$ for an inductor and, for a capacitor, the event is a change in voltage, \$\frac{dv}{dt}\$.- $$$$
- So, an inductor or capacitor will produce a proportional reaction (or response) to something changing. If we say that a capacitor **responds** to a change in voltage, we then have to define that **response** and, the only thing it **can do** is alter its current. Therefore we can say that the transfer function of a capacitor is: its response current (\$i\$) divided by its input (\$\frac{dv}{dt}\$) or this: -
- $$\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}$$
#15: Post edited
- "React" implies a response to an event. The event is a change in current, \$\frac{di}{dt}\$ for an inductor and, for a capacitor, the event is a change in voltage, \$\frac{dv}{dt}\$.
- $$$$
So, an inductor or capacitor will produce a rate-proportional reaction (or response) to something changing. If we say that a capacitor **responds** to a change in voltage, we then have to define that **response** and, the only thing it **can do** is alter its current. Therefore we can say that the transfer function of a capacitor is: its response current (\$i\$) divided by its input (\$\frac{dv}{dt}\$) or this: -- $$\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}$$
#14: Post edited
The word "react" implies that something responds to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.- $$$$
So, an inductor or capacitor will produce a proportional reaction (or response) to something changing at a fixed rate.$$$$If we say that a capacitor **responds** to a change in voltage, we then have to define that **response** and, the only thing it **can do** is alter its current. Therefore we can say that the transfer function of a capacitor is: its response current (\$i\$) divided by its input (\$\frac{dv}{dt}\$) or this: -- $$\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}$$
#13: Post edited
- The word "react" implies that something responds to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
- $$$$
An inductor or capacitor produces a proportional reaction to something changing at a fixed rate.- $$$$
- If we say that a capacitor **responds** to a change in voltage, we then have to define that **response** and, the only thing it **can do** is alter its current. Therefore we can say that the transfer function of a capacitor is: its response current (\$i\$) divided by its input (\$\frac{dv}{dt}\$) or this: -
- $$\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}$$
#12: Post edited
- The word "react" implies that something responds to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
- $$$$
The inductor or capacitor produces a fixed reaction to something that changes at a fixed rate.- $$$$
So, if we say that the output of a capacitor is **a reaction** to a change in voltage, we then have to state how it reacts and, the only thing it **can do** is alter the current flow. Therefore we can say that the transfer function of a capacitor is: its output current (\$i\$) over its input (\$\frac{dv}{dt}\$) or this: -- $$\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}$$
#11: Post edited
- The word "react" implies that something responds to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
- $$$$
The inductor or capacitor produces a fixed reaction to something that is changing at a fixed rate.- $$$$
- So, if we say that the output of a capacitor is **a reaction** to a change in voltage, we then have to state how it reacts and, the only thing it **can do** is alter the current flow. Therefore we can say that the transfer function of a capacitor is: its output current (\$i\$) over its input (\$\frac{dv}{dt}\$) or this: -
- $$\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}$$
#10: Post edited
- The word "react" implies that something responds to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
- $$$$
And, of course you can't define a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is producing a fixed reaction to something that is changing at a fixed rate.- $$$$
- So, if we say that the output of a capacitor is **a reaction** to a change in voltage, we then have to state how it reacts and, the only thing it **can do** is alter the current flow. Therefore we can say that the transfer function of a capacitor is: its output current (\$i\$) over its input (\$\frac{dv}{dt}\$) or this: -
- $$\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}$$
#9: Post edited
- The word "react" implies that something responds to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
- $$$$
And, of course you can't define a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing.- $$$$
So, if we say that the output of a capacitor is **a reaction** to a change in voltage, we then have to state how it reacts and, the only thing it **can do** is alter the current flow. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -- $$\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}$$
#8: Post edited
The word "react" implies that something responds to an event change. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.- $$$$
- And, of course you can't define a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing.
- $$$$
- So, if we say that the output of a capacitor is **a reaction** to a change in voltage, we then have to state how it reacts and, the only thing it **can do** is alter the current flow. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -
- $$\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}$$
#7: Post edited
- The word "react" implies that something responds to an event change. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
- $$$$
And, of course you can't measure a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing; there is a _"reactance"_.- $$$$
So, if we say that the output of a capacitor is **a reactance** to a change in voltage we then have to state how it reacts and, the only thing it **can do** is alter current. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -- $$\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}$$
#6: Post edited
"Reactance" is a word that is similar to "resistance" but, it's not the same; there is a subtle difference. The word "react" implies that something "reacts" to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.- $$$$
- And, of course you can't measure a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing; there is a _"reactance"_.
- $$$$
- So, if we say that the output of a capacitor is **a reactance** to a change in voltage we then have to state how it reacts and, the only thing it **can do** is alter current. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -
- $$\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}$$
#5: Post edited
- "Reactance" is a word that is similar to "resistance" but, it's not the same; there is a subtle difference. The word "react" implies that something "reacts" to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
- $$$$
- And, of course you can't measure a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing; there is a _"reactance"_.
- $$$$
- So, if we say that the output of a capacitor is **a reactance** to a change in voltage we then have to state how it reacts and, the only thing it **can do** is alter current. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -
- $$\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}$$
#4: Post edited
- "Reactance" is a word that is similar to "resistance" but, it's not the same; there is a subtle difference. The word "react" implies that something "reacts" to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
- $$$$
- And, of course you can't measure a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing; there is a _"reactance"_.
- $$$$
- So, if we say that the output of a capacitor is **a reactance** to a change in voltage we then have to state how it reacts and, the only thing it **can do** is alter current. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -
- $$\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}$$
#3: Post edited
- "Reactance" is a word that is similar to "resistance" but, it's not the same; there is a subtle difference. The word "react" implies that something "reacts" to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.
- $$$$
And, of course you can't measure a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing.- $$$$
- So, if we say that the output of a capacitor is **a reactance** to a change in voltage we then have to state how it reacts and, the only thing it **can do** is alter current. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -
$$\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}$$
#2: Post edited
"Reactance" is a word that is similar to "resistance" but, it's not the same; there is a subtloe difference. The word "react" implies that something "reacts" to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$.- $$$$
- And, of course you can't measure a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing.
- $$$$
- So, if we say that the output of a capacitor is **a reactance** to a change in voltage we then have to state how it reacts and, the only thing it **can do** is alter current. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: -
- $$\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}$$
#1: Initial revision
"Reactance" is a word that is similar to "resistance" but, it's not the same; there is a subtloe difference. The word "react" implies that something "reacts" to an event. For an inductor, the event is a change in current, \$\frac{di}{dt}\$ and, for a capacitor, the "event" is a change in voltage, \$\frac{dv}{dt}\$. $$$$ And, of course you can't measure a \$\frac{dx}{dt}\$ event in **zero time** hence, the inductor or capacitor is "reacting" to something that is changing. $$$$ So, if we say that the output of a capacitor is **a reactance** to a change in voltage we then have to state how it reacts and, the only thing it **can do** is alter current. Therefore we can say that the transfer function of a capacitor is its output (current) over input (\$\frac{dv}{dt}\$) or this: - $$\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}$$