Fall 2012

Physics 121 Practice Problem Solutions 12Inductance

Contents:

121P11 - 40P, 42P, 45P, 46P, 47P, 48P, 49P, 51P, 53P, 54P, 55P

• Inductors and Inductance

• Self-Inductance

• RL Circuits – Current Growth

• RL Circuits – Current Decay

• Energy Stored in a Magnetic Field

• Energy Density of a Magnetic Field

• Mutual Inductance

Fall 2012

PROBLEM 121P11-40P*: At a given instant the current and self-induced emf in an inductor are directed as indicated the figure . (a) Is the current increasing or decreasing? (b) The induced emfis 17 V and the rate of change of the current is 25 kA/s; find the inductance.

Fall 2012

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 ΩΩΩΩ. 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.)

Fall 2012

PROBLEM 121P11-45P: In terms of ττττL, how long must we wait for the current in an RL circuit to build up to within 0.100% of its equilibrium value?

Fall 2012

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.

Fall 2012

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.

Fall 2012

Consider the RL circuit of the sketch. In terms of the battery emf , (a) what is the self-induced

emfL

when the switch has just been closed on a, and (b) what is L

when t = 2.0ττττL? (c) In

terms of ττττL, when will L

be just one-half the battery emf ?

Problem 121P11-48

R

Fall 2012

PROBLEM 121P11-49: A solenoid having an inductance of 6.30 µµµµH is connected in series with a 1.20 kΩΩΩΩ 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 ττττL?

Problem 121P11-49

Fall 2012

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 ΩΩΩΩ. At what rate is the current increasing at t = 1.20 ms?

Fall 2012

PROBLEM 121P11-53: In the figure, = 100 V, R1 = 10.0 ΩΩΩΩ, R2 = 20.0 ΩΩΩΩ, R3 = 30.0 ΩΩΩΩ, 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 2012

PROBLEM 121P11-54: In the circuit shown below , = 10 V, R1

= 5.0 ΩΩΩΩ, R2

= 10 ΩΩΩΩ, 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 i

1

through R1, (b) the current i

2through R

2, (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 di

2/dt.

Fall 2012

PROBLEM 121P11-55P: In the circuit shown below, 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.