# Solve RC Circuits: Instantaneous Voltage in Capacitors

• abk80
In summary, the instantaneous value of voltage in a capacitor at any specific instant in time can be calculated using the fundamental equation i(t) = C\frac{dv(t)}{dt}. By either differentiating v(t) or integrating i(t), you can solve for the voltage across the capacitor. In a series RC circuit, the solution for the voltage across the capacitor is v(t) = V_i * (1-e^{\frac{-t}{RC}}), where the "1-" term accounts for the exponential approach of the capacitor voltage to the full input voltage. Additional resources, such as the Wikipedia page on RC circuits, can also aid in understanding this concept.
abk80
[SOLVED] Help with RC circuits

Can someone explain how to find the intantaneous value of voltage in a capacitor at any specific instant in time. I am taking a course in electronics and the textbook isn't really clear on this. I have the equation:
-t/T
Vc=E(1-e )
t=RC
Not sure why I am subracting from one. And why the negative symbols. I am sure this question is nonsense to an engineer or tech but I am stuck. Thanks

The fundamental equation to use when calculating the voltages and currents for a capacitor is the following:

$$i(t) = C\frac{dv(t)}{dt}$$

If you know the v(t) for the capacitor, you differentiate to get the i(t). If you know the i(t) for the capacitor, you integrate to get the v(t).

If you have a step change in current, you can solve the differential equation assuming a solution of the form:

$$v(t) = Ve^{\frac{-t}{\tau}}$$ subject to initial conditions, and where tau is related to the R and C values in the circuit.

So when you solve this differential equation for a series RC circuit where there is a step change in voltage across the whole RC, you end up with a solution for the voltage across the capacitor that looks something like:

$$v(t) = V_i * (1-e^{\frac{-t}{RC}})$$

You get the "1-" term, because the capacitor voltage exponentially approaches the full input voltage. If instead you were discharging the capacitor through a resistor, then you don't get the "1-" term.

This page at wikipedia.org may be of help to you too: http://en.wikipedia.org/wiki/RC_circuit

Welcome to the PF!

Last edited:
thank you that really helped.

## What is the equation for calculating instantaneous voltage in capacitors?

The equation for calculating instantaneous voltage in capacitors is Vc = V0(1 - e^(-t/RC)), where Vc is the instantaneous voltage, V0 is the initial voltage, t is the time, R is the resistance, and C is the capacitance.

## How do I calculate the time constant for a RC circuit?

The time constant for a RC circuit can be calculated by multiplying the resistance (R) by the capacitance (C). The unit for time constant is seconds (s).

## What happens to the voltage in a capacitor as time increases?

As time increases, the voltage in a capacitor will approach the maximum value of the voltage source. This means that the voltage in a capacitor will eventually reach the same value as the voltage source.

## How does the resistance affect the voltage in a capacitor?

The resistance in a RC circuit affects how quickly the voltage in a capacitor reaches its maximum value. A higher resistance will result in a slower increase in voltage, while a lower resistance will result in a quicker increase in voltage.

## Can the instantaneous voltage in a capacitor ever exceed the voltage source?

No, the instantaneous voltage in a capacitor can never exceed the voltage source. This is because the capacitor will eventually reach the same voltage as the source, and it cannot hold a higher voltage than the source.

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