Physics 121 Practice Problem Set 12 Inductance

Physics 121 Practice Problem Set 12
121P11 - 40P, 42P, 45P, 46P, 47P, 48P, 49P, 51P, 53P, 54P, 55P
Inductors and Inductance
RL Circuits – Current Growth
RL Circuits – Current Decay
Energy Stored in a Magnetic Field
Energy Density of a Magnetic Field
Mutual Inductance
Fall 2008
PROBLEM 121P11-40P*: At a given instant the current and self-induced emf in an inductor are directed
as indicated in the figure. (a) Is the current increasing or decreasing? (b) The induced emf is 17 V and
the rate of change of the current is 25 kA/s; find the inductance.
PROBLEM 121P11-42P: The current i through a 4.6 H inductor varies with time t as shown by the graph
in the figure. The inductor has a resistance of 12 Ω. Find the magnitude of the induced emf
during the
time intervals (a) t = 0 to t = 2 ms, (b) t = 2 ms to t = 5 ms, (c) t = 5 ms to t = 6 ms. (Ignore the behavior at
the ends of the intervals.)
PROBLEM 121P11-45P: In terms of τL, how long must we wait for the current in an RL
circuit to build up to within 0.100% of its equilibrium value?
Fall 2008
PROBLEM 121P11-46P*: The current in an RL circuit builds up to one-third of its steady-state value in
5.00 s. Find the inductive time constant.
PROBLEM 121P11-47P*: The current in an RL circuit drops from 1.0 A to 10 mA in the first second
following removal of the battery from the circuit. If L is 10 H, find the resistance R in the circuit.
PROBLEM 121P11-48P: Consider the RL circuit shown i the figure. In terms of the battery emf , (a)
what is the self-induced emf
L when the switch has just been closed on a, and (b) what is
L when t
= 2.0τL? (c) In terms of τL, when will
L be just one-half the battery emf ?
PROBLEM 121P11-49: A solenoid having an inductance of 6.30 µH is connected in series with a 1.20 kΩ
resistor. (a) If a 14.0 V battery is switched across the pair, how long will it take for the current through the
resistor to reach 80.0% of its final value? (b) What is the current through the resistor at time t = 1.0 τL?
Fall 2008
PROBLEM 121P11-51: At time t = 0, a 45.0 V potential difference is suddenly applied to a coil with L =
50.0 mH and R = 180 Ω. At what rate is the current increasing at t = 1.20 ms?
PROBLEM 121P11-53: In the figure,
= 100 V, R1 = 10.0 Ω, R2 = 20.0 Ω, R3 = 30.0 Ω, and L = 2.00
H. Find the values of i1 and i2 (a) immediately after the closing of switch S, (b) a long time later, (c)
immediately after the reopening of switch S, and (d) a long time after the reopening.
Fall 2008
PROBLEM 121P11-54: In the circuit shown,
= 10 V, R1 = 5.0 Ω, R2 = 10 Ω, and L = 5.0 H. For the two separate
conditions (I) switch S just closed and (II) switch S closed for a long time, calculate (a) the current i1 through R1, (b) the
current i2 through R2, (c) the current i through the switch, (d) the potential difference across R2, (e) the potential difference
across L, and (f) the rate of change di2/dt.
PROBLEM 121P11-55P: In the circuit shown, switch S is closed at time t = 0. Thereafter, the constant
current source, by varying its emf, maintains a constant current i out of its upper terminal. (a) Derive an
expression for the current through the inductor as a function of time. (b) Show that the current through
the resistor equals the current through the inductor at time t = (L/R) ln 2.
Fall 2008