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PHYS 196 Home Work 8
1. Find the potential difference DV = VB -VA in the following circuit elements:
A
A
B
4A
B
4A
5Ω
A
B
3V
5Ω
4A
R
I
A
5Ω
A
B
3V
5Ω
4A
B
Е
2. In the circuit shown, find (a) the current through the resistance R, (b) the potential difference
DV = VB -VA , and (c) the value of R.
3. For the circuit shown, find (a) the current in each resistor, (b) the power supplied by each source of emf,
and (c) the power delivered to each resistor.
4. In the circuit shown, the battery is ideal. Find (a) the current in each branch of the circuit, (b) the
potential difference between point a and point b, (c) the power supplied by each battery.
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5. Do the same as problem 4 for the following circuit:
6. For the circuit shown, find the potential difference between point a and point b, where point a is between
the 1  resistors at the top and b is between the 1  resistors at the bottom of the circuit. (a and b are
defined at similar locations as Problem 5)
7. For the circuit shown, find the current in the 5Ω resistor.
8. You are given a galvanometer that will deflect a full scale if a current of 50.0 A runs through it. At that
current, there is a voltage drop of 0.250V across the meter. (a) What is the internal resistance of the
galvanometer? (b) You wish to use the galvanometer to construct an ammeter that can measure currents
up to 100mA . Show that this can be done by placing a resistor in parallel with the meter, and find the
value of its resistance. (c) You wish to use the galvanometer to construct a voltmeter that can measure
potential difference up to 10.0V . Show that this can be done by placing a large resistor in series with the
meter, and find the value of its resistance.
9. Solve the differential equations with the indicated initial conditions:
2
(a)
dx
 5 x  0 x0  8
dt
(b)
dx
 5 x  10 x0   0
dt
(c)
dx
 5 x  10 x0   4
dt
10. A 20F capacitor is connected in series with a 160 resistor. The capacitor is initially charged to a
voltage of 50V . Find how long it takes for the voltage to drop to 10V .
11. A 20F capacitor is connected in series with an unknown resistor. The capacitor is initially charged to
50V . The voltage drops to 10V after 8.0ms . Find the unknown resistance.
12. A 12.0V ideal battery is used to charge up a 5.0µF capacitor via a 1.2MΩ resistor. Find how long it
takes for the voltage on the capacitor to reach 8.0V.
13. In the diagram for this problem, C  6.0F , R  5.0, I  2.0 A, Q  18C .
Find the potential difference V  VB  VA in the circuit element:
+Q
-Q
A
B
I
R
C
14. In the diagram for this problem, C  6.0F , R  5.0, Q  18C at the time when the switch is closed.
(a) Find the current I immediately after the switch is closed.
(b) Find the current I and the voltage V on the capacitor a long time after the switch is closed.
+Q
-Q
I
R
C
15. In the diagram for this problem, C  6.0F , R  5.0, I  2.0 A, Q  18C and the EMF of the ideal
battery is 12V . Find the potential difference V  VB  VA in the circuit element:
+Q
-Q
I
C
R
B
A
16. In the diagram for this problem, C  6.0F , R  5.0, Q  18C and the EMF of the battery is 12V at
the time when the switch is closed.
(a) Find the current I immediately after the switch is closed.
(b) Find the current I and the voltage V on the capacitor a long time after the switch is closed.
3
+Q
-Q
I
C
R
17. In the circuit below, the emf is 50.0V and the capacitance is 2.00µF. Switch S is opened after having
been closed for a long time., and 4.00s later the voltage drop across the resistor is 20.0V. Find (a) the
voltage on the capacitor right after the switch is closed, (b) the resistance of the resistor, (c) the current
through the resistor right after the switch is open.
S
18. In the same circuit as the previous problem, the emf of the ideal battery is 6.00V , the capacitance is
1.50 F and the resistance is 2.00M . Switch S has been closed for a long time. It is then open. After a
time interval equal to one time constant of the circuit, find (a) the charge on the capacitor plate on the
right, (b) the rate at which charge is increasing, (c) the current, (d) the power supplied by the battery, (e)
the power delivered to the resistor, and (f) the rate at which energy stored in the capacitor is increasing.
19. For the circuit as shown, C  6.00F ,   100V , and R  500 . After having been at contact a for a
long time, the switch throw is rotated to contact b . (a) What is the charge on the upper plate of the
capacitor just as the switch throw is moved to contact b ? (b) What is the current just after the switch
throw is rotated to contact b ? (c) What is the time constant of this circuit? (d) How much charge is on
the upper plate of the capacitor 6.00ms after the switch throw is rotated to contact b ?
a
b

R
C
20. Referring to the same circuit as the previous problem, where at t=0 the switch throw is rotated to contact
b having been in contact a for a long time, (a) How much energy is stored in the capacitor at t  0 ? (b)
For t  0 , find the energy stored in the capacitor as a function of time.
Answers:
1.  20V , 20V ,  17V , 17V ,   IR
2. 3A, -147V, 6.67W
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3. (a) 2 A, 1A (b) 16W , 8W ,  4W , (c) 4W , 8W , 2W , 6W
4. (a) 0.667A, 0.889A, 1.56A (b) 9.36V (c) 8W, 10.7W
5. (a) 3 A, 2 A, 1A (b)  1V (c) 21W , 10.W
6. 3.84V
7. 0.077 A
8. 5k, 2.5, 0.2M
9. (a) x  8e 5t (b) x  2 e 5t  1 (c) x  2 e 5t  1
10. 5.15ms
11. 250W
12. 6.59s
13. 7V
14. (a) 0.6 A, (b) 0 A, 0V
15.  1V
16. (a) 1.8 A (b) 0 A, 12V
17. 0V , 2.19M, 22.8A
18. 5.69C , 1.10C / s, 1.10A, 6.62W , 2.44W , 4.19W
19. 600C , 0.200 A, 3.00ms, 81.2C




20. 0.03J , 0.03e 2t 3 J
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