1. Electric Current and Direct-Current Circuits (Cont.)
Chapter 21
Electric Current and Direct-Current Circuits (Cont.)
Dr. Jie Zou
PHY 1161

2. Outline RC circuit Charging of an RC circuit Charge on a capacitor
Current in an RC circuit
Voltage across the resistor and capacitor
Dr. Jie Zou
PHY 1161

3. RC Circuits
The simplest example of a RC circuit consists of a battery, a resistor, and a capacitor.
The resistors limit the rate at which charge can flow, and an appreciable amount of time may be required before the capacitors become fully charged.
Dr. Jie Zou
PHY 1161

4. Charging of an RC Circuit
Initially (t<0) the switch is open, and there is no current in the resistor or charge on the capacitor.
At t=0, the switch is closed, and current begins to flow. The capacitor is being charged.
As time goes on, the charge on the capacitor increases but the charging slows down.
At t∞, the charge on the capacitor does not change with time and the current approaches zero.
Dr. Jie Zou
PHY 1161

5. Charge on the Capacitor
The charge on the capacitor varies with time as follows: q(t) = C(1-e -t/), for t >= 0
 = RC: the time constant of the RC circuit.
At t = 0, q(0) = 0
At t, q(t) = C (charging complete).
Dr. Jie Zou
PHY 1161

6. Current in an RC Circuit
The current in an RC circuit changes with time as follows: I(t) = (/R)e -t/, for t>= 0
At t = 0, I(0) = /R. The capacitor behaves like a short circuit.
At t, I(t) = 0. The capacitor behaves like an open switch.
Dr. Jie Zou
PHY 1161

7. Voltage across the Resistor and the Capacitor
Voltage across the resistor: VR = IR = e -t/.
At t = 0, VR(0) = 
At t, VR(t) = 0
Voltage across the capacitor VC:
VC =  - VR =  - e -t/ = (1- e -t/)
At t = 0, VC (0) = 0
At t, VC (t) = 
Dr. Jie Zou
PHY 1161

8. Example 21-9 Charging a Capacitor
A circuit consists of a 126- resistor, a 275- resistor, a 182-F capacitor, a switch, and a 3.00-V battery all connected in series. Initially, the capacitor is unchanged and the switch is open. At time t = 0 the switch is closed.
(a) What charge will the capacitor have a long time after the switch is closed?
(b) At what time will the charge on the capacitor be 80.0% of the value found in part (a)?
Dr. Jie Zou
PHY 1161

9. Homework #5
Chapter 21, P. 759, Problems: #79, 81 (Physics, Walker, 4th edition).
Dr. Jie Zou
PHY 1161