Chapter 30 Homework
Mutual Induction
Qu. 1 Two coils have a mutual inductance, M = 3.25 x 10-4 H. The current i1 in
the first coil increases at a uniform rate of 830 A/s. What is the magnitude of the
e.m.f induced in the second coil.
(Ans: e.m.f. = 0.27 V )
Qu. 2 Two coils are wound around the same cylindrical form as in Example 30.1.
When the current in the first coil is decreasing at a rate of -0.242 A/s the induced
e.m.f in the second coil has a magnitude 1.65 x 10-3 V.
a) What is the mutual inductance of the pair of coils?
(Ans: M =6.81 x 10-3 H)
b) If the second coil has 25 turns, what is the flux through each turn when the
current in the first coil equals 1.2 A? ( Ans: ϕ = 3.26 x 10-4 Wb).
c) If the current in the second coil increases at a rate of 0.36 A/s what is the
magnitude of the induced e.m.f. in the first coil ? (Ans: e.m.f. = 2.45 mV )
Qu. 3 Coil A has 5 turns of area 2.4 cm2 and coil B has 6 turns of area 0.5 cm2.
The planes of the coils coincide. When the current in coil A is 2A it produces an
essentially uniform B-field of 10 µT over the area of coli B.
a) Find the mutual inductance (Ans: M =1.5 x 10-9 H).
b) Find the e.m.f induced in coli A when the current in coil B changes at 40 A/s.
(Ans: 6.0 x 10-8 V).
Self Induction
Qu. 4 The self-induced e.m.f in a solenoid of length 25cm and radius 1.5 cm is 1.6
mV when the current is 3 A and increasing at the rate of 200 A/s.
a) What is the number of turns? (Ans: N = 47.5 turns)
b) What is the B-field within the solenoid at the given instant ?
(Ans: B = 7.14 x 10-4 T)
R-L Circuits
Qu. 5 In the circuit shown below, S2, is open and S1 is closed at t=0 s. Find
a) the current after 50 ms. (Ans: i = 0.28 A)
b) the e.m.f in the inductor after 50 ms (Ans: ε = 10.33 V)
c) the time needed for the current to reach 80% of its final value. (Ans: t = 0.53 s)
R=6Ω
S1
12 V +
S2
L=2H
Qu. 6 In the circuit shown below S1 has been closed for a long time. At t=0s, S2 is
closed and S1 is opened. Find
a) at what time does the potential difference across the resistor drop to 12.5% of its
initial value? (Ans; t = 0.693 s)
b) what is the e.m.f in the inductor at the time found in part a) (Ans: ε = -1.5 V)
R=6Ω
S1
12 V +
S2
L=2H
Power in R-L Circuits
A resistor, R = 5Ω, is in series with an inductor L = 40 mH and a 20V battery. The
switch is closed at t=0. At what time will the power loss in R equal the rate at which
energy is being stored in L? Express your answer in terms of the number of time
constants. (Ans: t = 0.69τ)
L-C Circuits
The minimum capacitance of a variable capacitor in a radio is 4.18 pF.
a) What is the inductance of a coil connected to this capacitor if the oscillation frequency
of the L-C circuit is 1.6 x 106 Hz, corresponding to one end of the AM radio broadcast
band, when the capacitor is set to its minimum capacitance? (Ans: L = 2.36 mH)
b) The frequency at the other end of the AM broadcast band is 5.4 x 105 Hz. What is the
maximum capacitance of the capacitor if the oscillation frequency is adjustable over the
range of the broadcast band? (Ans: C = 36.7 pF).