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Chapter 21
Electric Current and DirectCurrent Circuits (Cont.)
Dr. Jie Zou
PHY 1161
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Outline
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RC circuit
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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
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RC Circuits
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Dr. Jie Zou
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.
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Charging of an RC Circuit
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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
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Charge on the Capacitor
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The charge on the capacitor
varies with time as follows:
q(t) = C(1-e -t/), for t >= 0
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Dr. Jie Zou
 = RC: the time constant of
the RC circuit.
At t = 0, q(0) = 0
At t, q(t) = C (charging
complete).
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Current in an RC Circuit
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The current in an RC circuit
changes with time as
follows: I(t) = (/R)e -t/, for
t>= 0
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Dr. Jie Zou
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.
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Voltage across the Resistor
and the Capacitor
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Voltage across the resistor: VR = IR = e
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-t/.
At t = 0, VR(0) = 
At t, VR(t) = 0
Voltage across the capacitor VC:
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VC =  - VR =  - e -t/ = (1- e
At t = 0, VC (0) = 0
At t, VC (t) = 
Dr. Jie Zou
PHY 1161
-t/)
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Example 21-9 Charging a
Capacitor
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A circuit consists of a 126-
resistor, a 275- resistor, a 182F capacitor, a switch, and a 3.00V battery all connected in series.
Initially, the capacitor is
unchanged and the switch is open.
At time t = 0 the switch is closed.
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(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
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Homework #5
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Chapter 21, P. 759, Problems: #79, 81
(Physics, Walker, 4th edition).
Dr. Jie Zou
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