Download HW16 - University of St. Thomas

Physics 112 HW16
/6
Due Wednesday, 22 October 2014
RC01. Consider the circuit at right. The capacitor is initially charged
so that the voltage across it is 10 V. The switch is closed at t = 0s.
Calculate what R must be so that the capacitor is 90% discharged
(10% of the original charge is left) in
a) 10 ms,
b) 10 s, and
c) 10,000 s.
RC02. In the circuit at right, the battery is ideal (no internal resistance)
and the capacitor is initially uncharged. Calculate the value of C if the
capacitor is 50% charged up
a) 10 ms,
b) 1 s, and
c) 100 s after closing the switch.
RC03. In the circuit at right, the capacitors are initially
uncharged. How long after the switch is closed does the
current go down to 20% of its original value? Your answer
will be in terms of R and C.
R
C = 1 μF
100 Ω
10V
(ideal)
C
R
R
V
(ideal)
C
R
C
C
RC04. Initially, the capacitor in the circuit at right is uncharged and
switch in
the switch is in position 2. The switch is put into position 1 so that
position 2
switch in
the capacitor begins to charge. After the switch has been in position
position 1
1 for 10.0 ms, the switch is moved back to position 2 so that the
capacitor begins to discharge.
15.0 μF
18.0 V
a) Compute the charge on the capacitor just before the switch is
(ideal)
thrown from position 1 to position 2.
b) Compute the voltages across the resistor and across the
capacitor at the instant described in part (a).
980 Ω
c) Compute the voltages across the resistor and across the
capacitor just after the switch is thrown from position 1 to position 2.
d) Compute the charge on the capacitor 10.0 ms after the switch is thrown from position 1 to position
2.
RC05. (Toughie?) Consider the circuit at right. This convention is
V = 18.0 V
often used in circuit diagrams. The battery (or other power
supply) is not shown explicitly. It is understood that the point at
the top, labeled “18.0 V,” is connected to the positive terminal of
6.00 μF
a 18.0 V battery having negligible internal resistance, and that the
6.00 Ω
ground symbol at the bottom is connected to the negative terminal
a
b
of the battery. The circuit is completed through the battery, even
3.00 Ω
though it is not shown on the diagram.
3.00 μF
a) What is the potential of point a with respect to point b when
the switch is open? (The circuit has been like this for a long
time.)
b) Which point, a or b, is at the higher potential?
c) What is the final potential of point b with respect to ground when the switch is closed?
d) How much does the charge on each capacitor change long after the switch is closed?
(over)
RC06. (Toughie?) In the circuit shown at right, the capacitor is
originally uncharged with the switch open. At t = 0 the switch is
C
closed.
V
R2
a) What is the current supplied by the battery just after the
(ideal)
R1
switch is closed?
b) What is the current a long time after the switch is closed?
c) Derive an expression for the current through the battery for any time after the switch is closed.
d) After a long time t’ the switch is opened. How long does it take for the charge on the capacitor to
decrease to 10 percent of its value at t = t’ if R1 = R2 = 5 kΩ and C = 1.0 μF?
(over)