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
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '09
 bak

Click to edit the document details