# Voltage drop across capacitor – formula and concepts

A Capacitor is one of the important components in electrical circuit. We have discussed on capacitors, their combinations and other related facts in other articles. Like other components (resistors, inductors), a capacitor also offer an opposition to the current flow through it. From the Ohm’s law, we get an expression for voltage drop across a resistor. Now, the question is: “Is there any voltage drop across a capacitor?” The answer is, “Yes“. But why? How to calculate the voltage across a capacitor? In this article, we are going to discuss all these things.

## Why is there a voltage drop across a capacitor?

A capacitor is just a neutral conductor in absence of external voltage source (before charging). But when an external voltage is applied across a capacitor, it begins to store electric charges inside it. Now, the voltage across a capacitor is directly proportional to the electric charge on it. The voltage across a capacitor changes due to change in charge on it. So, during charging of a capacitor, the voltage across it increases. When the capacitor is completely charged, the voltage across the capacitor becomes constant. Now, if we remove external battery, the discharging of the capacitor begins. During discharging of the capacitor, the voltage across it decreases and after a certain time, its voltage falls to zero.

## Formula for voltage drop across capacitor

1. The voltage across an uncharged capacitor is zero.
2. During charging a capacitor of capacitance C with a series resistor R, the equation for the voltage across a charging capacitor at any time t is V(t) = Vs (1 – e-t/τ), where τ=RC is the time constant in the series RC circuit and Vs is the maximum voltage of the external battery.
3. After a long time of charging, the capacitor reaches to the saturation condition. At this condition the voltage drop across it becomes maximum. The maximum voltage across a capacitor is Vs. But practically, the voltage across the capacitor cannot be as much as the maximum voltage of battery. It should be a possible voltage V0. If Q be the maximum charge on the capacitor, then the formula for maximum voltage across the capacitor is $\small {\color{Blue} V_{0} = \frac{Q}{C}}$. Then we get Q=CV0. This is a popular formula for the voltage across a capacitor.
4. Now, if the external battery is removed, the capacitor switches to discharging mode and the voltage drop across the capacitor starts to decrease. The voltage across the discharging capacitor becomes, V(t) = V0 e-t/τ.

## How to find voltage drop across a capacitor?

Above equations are useful for the finding of voltage across a capacitor. There are different formulae for the different situations. We need to use proper formula to find the voltage across a capacitor as our requirements.

1. Step-1: First identify the situation – whether the capacitor is charging or discharging or at saturation condition.
2. Step-2: Use the proper formula or equation according to the condition.
3. Step-3: Put the values of required quantities like R, C, time constant, voltage of battery and charge (Q), etc. in that equation.
4. Step-4: Calculate the value of the voltage from the equation.

## Examples

1. A battery of voltage 10 volt is connected across a circuit consisting a resistor of 100 ohm and a capacitor of 0.01 farad in series. If the capacitor is uncharged initially then find the voltage across the capacitor after 2 second.

Answer: In this case, the capacitor is in charging mode. So, the voltage drop across the capacitor is increasing with time.

The time constant, τ=RC=1, the maximum voltage of battery, Vs=10 volt and the time, t=2 second.

Now, using the equation for the charging capacitor, V(t) = Vs (1 – e-t/τ), we get the voltage across the capacitor after 2 second is, V=8.65 volt.

This is all from this article. If you have any doubt on this topic you can ask me in the comment section.

Thank you!

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