Problem Set 7
Due: See website for due dates
Chapter 27: Circuits
Problems: 1, 26 (challenging), 33, 39, 45, 61, 63, 72
Question A
Explain why an ideal ammeter would have zero resistance and an ideal voltmeter
infinite resistance?
Question B
Why do the lights on a car become dimmer when the starter is operated?
Question C
Why does current follow the path of least resistance in a parallel circuit?
Question D
Fish like electric eels have specially designed nerve cells that allow them to discharge
hundreds of volts of electricity. Now, while pure water is usually nonconductive, the
dissolved salts and other stuff in both sea and fresh water allow them to be conductive.
If an electric fish is able to use its electricity to stun enemies or prey, how come the fish
itself is unaffected? Hint: think parallel circuit.
Question E
The velocity of the electrons in the wires is very slow (few mm/s), but when one turns on
the light, one doesn't see any delay. Why?
Problem 27.1
The figure shows the ideal batteries have emfs 1 = 12 V and 2 = 6.0 V.
What are (a) the current, the dissipation rate in (b) resistor 1 (4.0 ) and
(c) resistor 2 (8.0 ), 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? Explain your answers! SSM.
Problem 27.26 (challenging)
The figure shows a battery connected across a uniform resistor R0. A sliding contact can move
across the resistor from x = 0 at the left to x = 10 cm 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 
Problem 27.33
In the figure, 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 27.39
In the figure, 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 27.45
In the figure, 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 direction (up or down) of the current in battery 1, the (b) size and
direction of the current in battery 2, and the (c) size and direction of the
current in battery 3? (d) What is the potential difference Va − Vb?
Problem 27.61
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 27.63
In the circuit,  =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 27.72
In the figure, 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?