Download HW15 - University of St. Thomas

Physics 112 HW15
/8
Due Monday, 24 October 2016
VIR01. The circuit at left consists of two batteries (the grey shaded
areas) broken up into ideal EMF sources with internal resistances,
along with two resistors.
a) What is the voltage difference between points a and d?
b) What is the terminal voltage across the 4 V battery? (What
is the voltage one would measure across it when it is put in
this circuit, or the voltage between points b and c?)
c) A battery with EMF 10.30 V and internal resistance 0.50 Ω
is inserted at point d in such a way that its negative terminal
(the box) is connected to the negative terminal of the 8.0V
battery. What is the terminal voltage across the 4 V battery
now?
4.00 V
b
c
0.50 Ω
9.00 Ω
d
6.00 Ω
a
8.00 Ω
0.50 Ω
8.00 V
150 kΩ
VIR02. Consider the circuit at right. The (non-ideal) voltmeter has a
resistance of 900 kΩ. Calculate the voltage the voltmeter reads (the
voltage across resistor R) if
20V
R
(ideal)
a) R = 10 Ω,
b) R = 10 kΩ, and
c) R = 10 MΩ.
d) Repeat parts a – c if the voltmeter is ideal (it has essentially infinite resistance). Does the finite
resistance of voltmeters matter?
V
VIR03. Consider the circuit at right. Both voltmeters and the ammeter are ideal; the “r” represents the
internal resistance of the battery. The switch is initially open,
and the voltmeter V1 reads 10 volts.
r
R1
a) What does ammeter A read?
A
V
o
V1
b) What does voltmeter V2 read?
c) What is the voltage of the battery’s ideal voltage source?
R2
The switch is now closed. V1 now reads 9V, V2 now reads 3V,
and the ammeter reads 0.5A.
d) Determine the values of r, R1, and R2.
Open the switch and replace the two voltmeters with crappy non-ideal voltmeters each with an internal
resistance of 100Ω. Also replace the ideal ammeter with a non-ideal ammeter with internal resistance
1Ω. The resistors r, R1, and R2 have the values you determined in part d above.
e) Determine what V1, V2, and A read now.
Close the switch.
f) Determine what V1, V2, and A read now.
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 in
a) 10 ms,
b) 1 s, and
c) 100 s after closing the switch.
V2
R
C = 1 μF
100 Ω
10V
(ideal)
C
RC04. Initially, the capacitor in the circuit at right is uncharged and the switch is in position 2. The switch
is put into position 1 so that the capacitor begins to charge. After the switch
switch in
has been in position 1 for 10.0 ms, the switch is moved back to position 2 so
position 2
switch in
that the capacitor begins to discharge.
position 1
a) Compute the charge on the capacitor just before the switch is thrown from
position 1 to position 2.
b) Compute the voltages across the resistor and across the capacitor at the
18.0 V
instant described in part (a).
(ideal)
c) Compute the voltages across the resistor and across the capacitor just after
the switch is thrown from position 1 to position 2.
980 Ω
d) Compute the charge on the capacitor 10.0 ms after the switch is thrown
from position 1 to position 2.
15.0
μF
RC05. (Toughie?) Consider the circuit at right. This convention is often used
V = 18.0 V
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 a 18.0 V battery having negligible
6.00 μF
6.00 Ω
internal resistance, and that the ground symbol at the bottom is connected to
the negative terminal of the battery. The circuit is completed through the
a
b
battery, even though it is not shown on the diagram.
3.00 Ω
a) What is the potential of point a with respect to point b when the switch
3.00 μF
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?
RC06. (Toughie?) In the circuit shown at right, the capacitor is originally
uncharged with the switch open. At t = 0 the switch is closed.
C
a) What is the current supplied by the battery just after the switch is closed?
V
b) What is the current a long time after the switch is closed?
(ideal)
R1
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?
Gustav R. Kirchhoff
1824-1887
R2