# Resistor-Capacitor (RC) Circuits: Practice Problems Video

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• 0:01 What Is an RC Circuit?
• 0:49 Equations
• 2:44 Practice Problems
• 4:36 Lesson Summary
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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this video, you will be able to calculate or deduce the current and voltage in the components of an RC circuit at the start of the charging process and when the capacitor is fully charged. A short quiz will follow.

## What is an RC Circuit?

An RC circuit, short for 'resistor-capacitor circuit,' is an electric circuit made up of resistors and capacitors connected to a voltage or current source. A basic RC circuit contains just one resistor and one capacitor.

RC circuits can help to filter a signal by blocking certain electrical frequencies. For this reason, they're used as high-pass, low-pass and band-pass filters in audio recordings like this one:

When you connect a resistor and a capacitor in a series circuit, the capacitor will charge up. The battery will transfer charge from one plate of the capacitor to the other, storing charge (and therefore energy) on the plates of the capacitor. But to really see what's happening and why, we need to look at some equations.

## Equations

In any circuit, including RC circuits, the voltage of a battery is a constant. You can't change it without changing the battery itself. And since we're looking at a series circuit, the voltage of the battery is also equal to the voltage across the resistor, plus the voltage across the capacitor. The voltage across the resistor is equal to IR, the current through the resistor, I, measured in amps, multiplied by the resistance of the resistor, R, measured in ohms. And the voltage across the capacitor is equal to Q over C, where Q is the charge on the capacitor measured in coulombs, and C is the capacitance of the capacitor in farads. We're going to call this the RC voltage equation. As the capacitor charges, the charge Q will increase, and so the current I must decrease to compensate. This is because the voltage of the battery must be constant.

This reflects what we see: as a capacitor charges, the current in the circuit slows until it nears zero. At this point the circuit has reached a steady state. The capacitor is fully charged and ready to be discharged by connecting it to another circuit component in a complete loop.

But how do we calculate the voltage and current at various points in this process?

Well, when you first close the switch and start the charging process, the charge on a capacitor, Q, equals zero, and the voltage across the resistor will therefore be equal to the voltage of the battery. To find the current flowing through the circuit, just use V=IR, where V is the voltage of the battery, and R is the resistance of the resistor, and solve for I.

At the end, when the capacitor is fully charged, the current has gradually reduced and is approaching zero. Since the current is zero, the 'IR' part of the RC voltage equation is equal to zero. So the voltage across the capacitor must be equal to the voltage of the battery.

## Practice Problems

Practice Problem Part 1: A 12-ohm resistor is connected in series with a 6-volt battery and a 5-farad capacitor. What is the voltage across the resistor and capacitor when you first connect the circuit? And what is the voltage across them when the capacitor is fully charged?

First of all, we should write down what we know. The resistance of the resistor, R, is 12. The voltage of the battery, Vb, is 6. And the capacitance of the capacitor is 5.

We can answer this first question using some conceptual understanding. When we first connect the circuit, there is no charge on the capacitor. So the voltage across the capacitor (Q over C) will be zero. This means that the voltage across the resistor must be equal to the full voltage of the battery: 6 volts. So the voltage across the capacitor is 0 volts, and the voltage across the resistor is 6 volts.

And when the capacitor is fully charged, the current, I, will be zero. This means that the voltage across the resistor (I times R) will be zero. So the capacitor must be taking up the full voltage of the battery: 6 volts. So the voltage across the capacitor is 6 volts, and the voltage across the resistor is 0 volts.

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