HPHY 253 Workout 28b
Series RC Circuits
Dr. A. E. Bak
Name
If a capacitor of capacitance
C
is being charged by a voltage source of electromotance
E
through a resistor
of resistance
R
Q
varies with time according to the relation
Q
(
t
) =
Q
max
1
e
±
for a charging capacitor
;
where
Q
max
=
C
E
is the maximum possible charge that the capacitor can acquire. The quantity
±
RC
is
time constant
. If a charged capacitor is discharging through a resistor, then we have
Q
(
t
) =
Q
0
e
for a discharging capacitor
;
where
Q
0
is the initial charge on the capacitor.
On de±ning the capacitor current
I
C
as
I
C
±
²
²
²
²
dQ
dt
²
²
²
²
;
we ±nd that
I
C
=
Q
max
e
=
E
R
e
for a charging capacitor
and
I
C
=
Q
0
e
for a discharging capacitor
:
Note that
dQ=dt
is the time rate at which the capacitor acquires charge.
1.
28
:
27
. Consider the series
RC
circuit of Active Figure
28
:
16
, for which
R
= 1
:
00
M
,
C
= 5
:
00
±F
, and
E
= 30
:
0
V
.
(a)
Find the time constant of the circuit.
We have
=
RC
=
³
1
:
00
²
10
6
´ ³
5
:
00
²
10
6
´
= 5
:
00
s
as the time constant.
(b)
Find the maximum charge on the capacitor after the switch is thrown to position
a
, thereby
connecting the capacitor to the battery.
We have
Q
max
=
C
E
=
³
5
:
00
²
10
6
´
(30
:
0) = 1
:
50
²
10
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 Spring '09
 bak
 Electric charge, RC circuit, Qmax

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