Download Problem Set 7

Problem Set 7
Due: 10/27/09, Tuesday
Chapter 27: Circuits
Exercises & Problems: 7, 14 (challenging), 31, 37, 41, 59, 65, 82
Chapter 27 Even Answers
100R  x R0 
2
100R R
0
 10x  x 2

2
; 3.0 A, 10 A, 13 A, 1.5 A, 7.5 A;
Question A
Why do the lights on a car become dimmer when the starter is operated?
Question B
Two 120-V lightbulbs, one 25-W and one 200-W, were connected in series
across a 240-V line. It seemed like a good idea at the time, but one bulb burned
out almost instantaneously. Which one burned out, and why?
Question C
Explain why an ideal ammeter would have zero resistance and an ideal voltmeter
infinite resistance?
Question D
A capacitor is connected across the terminals of a battery. Does the amount of
charge that eventually appears on the capacitor plates depend on the internal
resistance of the battery?
Problem 27.7
In Fig. 27-26, the ideal batteries have emfs 1 = 12 V and 2 = 6.0 V and
the resistors have resistances R1 = 4.0  and R2 = 8.0 . What are (a)
the current, the dissipation rate in (b) resistor 1 and (c) resistor 2, and the
energy transfer rate in (d) battery 1 and (e) battery 2? Is energy being
supplied or absorbed by (f) battery 1 and (g) battery 2? SSM.
Problem 27.14
Figure 27-31 shows a battery connected across a uniform resistor R0. A sliding contact
can move across the resistor from
at the left to
at the
right. Moving the contact changes how much resistance is to the left
of the contact and how much is to the right. Find the rate at which
energy is dissipated in resistor R as a function of x. Plot the function
for  = 50 V, R = 2000 andR0 = 100 
1
Problem 27.31
In Fig. 27-42, the current in resistance 6 is i6 =
1.40 A and the resistances are R1 = R2 = R3 =
2.00 , R4 = 16.0 , R5 = 8.00  and R6 = 4.00
. What is the emf of the ideal battery?
Problem 27.37
In Fig. 27-48, the resistances are R1 = 1.0  and R2 = 2.0 , and the
ideal batteries have emfs 1 = 2.0 V and 2 = 3 = 4.0 V. What are the (a)
size and (b) direction (up or down) of the current in battery 1, the (c) size
and (d) direction of the current in battery 2, and the (e) size and (f)
direction of the current in battery 3? (g) What is the potential difference Va
− Vb?
Problem 27.41
In Fig. 27-52, two batteries of emf  = 12.0 V and internal resistance r = 0.300 
are connected in parallel across a resistance R. (a) For what value of R is the
dissipation rate in the resistor a maximum? (b) What is that maximum?
Problem 27.59
A 15.0 kΩ resistor and a capacitor are connected in series, and then a 12.0 V potential
difference is suddenly applied across them. The potential difference across the capacitor
rises to 5.00 V in 1.30 μs. (a) Calculate the time constant of the circuit. (b) Find the
capacitance of the capacitor.
Problem 27.65
In the circuit of Fig. 27-64,  1.2 kVC = 6.5FR1 = R2 = R3 = 0.73
M. With C completely uncharged, switch S is suddenly closed (at t =
0). At t = 0, what are (a) current i1 in resistor 1, (b) current i2 in resistor
2, and (c) current i3 in resistor 3? At t =  (that is, after many time
constants), what are (d) i1 (e) i2, and (f) i3? What is the potential
difference V2 across resistor 2 at (g) t = 0 and (h) t =  ? (i) Sketch V2
versus t between these two extreme times. SSM
Problem 27.82
In Fig. 27-74, the ideal battery has emf  30.0
Vand the resistances are R1 = R2 = 14 , R3 = R4
= R5 = 6.0 , R6 = 2.0 , and R7 = 1.5 . What are
currents (a) i2, (b) i4, (c) i1, (d) i3, and (e) i5?
2