RC Circuits

Friday 7-12-96

Homework Problems : 60, 61

The relevant section in the textbook is 17.3

Main concepts:

• Resistors are relatively simple circuit elements, in that when a resistor or a set of resistors is connected to a voltage source in a circuit, the current that flows maintains a constant value. If a capacitor is added to the circuit, the situation changes. In a direct current (DC) circuit, the current will follow an exponential decay. The time it takes to decay is determined by the resistance (R) and capacitance (C) in the circuit.

• Recall that a capacitor is a device for storing charge. In some sense, a capacitor acts like a temporary battery. When a capacitor is connected through a resistor to a battery, charge from the battery is stored in the capacitor. This causes a potential difference to build up across the capacitor, a potential difference that opposes the potential difference of the battery. As this potential difference builds, the current in the circuit decreases.

• If the capacitor is connected to a battery with a voltage (i.e., potential difference) of Vo, the voltage across the capacitor varies with time according to the equation:

  V = Vo [1 - e^(-t/RC)]

• The current in the circuit varies with time according to the equation:

  I = Io e^(-t/RC)

• Note that the product of the resistance and capacitance, RC, in the circuit is known as the time constant. This is a measure of how fast the capacitor will charge or discharge.

• After charging a capacitor with a battery, the battery can be removed from the circuit and the capacitor can be used to supply current to the circuit. In this case, the current obeys the same equation as above, decaying away exponentially, and the voltage across the capacitor will vary as:

  V = Vo e^(-t/RC)