RC TIME CONSTANT

NOTE: Check with the laboratory instructor before plugging in power supply AND before disconnecting your circuit.

Arrange the capacitor, switch power supply, resistor box, and ammeter as shown in the circuit below. When the switch is closed to one pole, the power supply V charges the capacitor. When the power supply is then switched to "standby" and the circuit switch is opened, the capacitor is charged. Upon closing the switch to the opposite pole, the capacitor discharges with a surge of current. This current decays exponentially.

When the capacitor is fully charged, there is a voltage of V = 12 volts across the capacitor. When the RC circuit is activated the charge flows through the resistor and ammeter with a current i = -, where Q is the instantaneous charge on the capacitor. The voltage across the capacitor is V = , and is equal to the voltage across the resistor

V = iR. One therefore obtains the differential equation:

iR = -R, or

This can be integrated to yield

Q = Q0

where t = RC is called the RC time constant. The instantaneous current is given by

i = i0

where i0 = 

Let t10 denote the time at which the instantaneous current i is equal to  the initial current i0. This then gives

t10 = t ln 10 = RC ln 10.

Set the power supply to 12 V. Set the ammeter on the 50 mA scale. Set the resistor box to 500 W. Charge the capacitor.

CAUTION: NEVER accidentally short circuit the capacitor with your hand or any other material!

Put the power supply on "standby" and carefully open the circuit switch. The capacitor is now charged. Carefully close the circuit switch to discharge the capacitor through the resistor and ammeter, and note the initial surge current i0. Calculate i10 =  . Recharge the capacitor, and again discharge it, this time measuring t10. Obtain several measurements of t10, and calculate the average value. Compare the experimentally measured value of t10 with that predicted in the last equation.

Last Updated: 4 Jan 2001
http://www.iun.edu//~woz/p2web/rctime/rctime.htm
Comments: Laboratory Supervisor
Copyright 1999, The Trustees of Indiana University