Physics 121 Practice Problem Solutions 12 Inductance Contents

Physics 121 Practice Problem Solutions 12 Inductance Contents: 121 P 11 - 40 P, 42 P, 45 P, 46 P, 47 P, 48 P, 49 P, 51 P, 53 P, 54 P, 55 P • • 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 Spring 2020

PROBLEM 121 P 11 -40 P*: 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 emf is 17 V and the rate of change of the current is 25 k. A/s; find the inductance. Spring 2020

PROBLEM 121 P 11 -42 P: 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 W. 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. ) Spring 2020

PROBLEM 121 P 11 -45 P: In terms of t. L, how long must we wait for the current in an RL circuit to build up to within 0. 100% of its equilibrium value? Spring 2020

PROBLEM 121 P 11 -46 P*: 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. Spring 2020

PROBLEM 121 P 11 -47 P*: The current in an RL circuit drops from 1. 0 A to 10 m. A in the first second following removal of the battery from the circuit. If L is 10 H, find the resistance R in the circuit. Spring 2020

Problem 121 P 11 -48 Consider the RL circuit of the sketch. 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. 0 t. L? (c) In terms of t. L, when will L be just one-half the battery emf ? R Spring 2020

PROBLEM 121 P 11 -49: A solenoid having an inductance of 6. 30 m. H is connected in series with a 1. 20 k. W 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 t. L? Spring 2020

PROBLEM 121 P 11 -51: At time t = 0, a 45. 0 V potential difference is suddenly applied to a coil with L = 50. 0 m. H and R = 180 W. At what rate is the current increasing at t = 1. 20 ms? Spring 2020

PROBLEM 121 P 11 -53: In the figure, = 100 V, R 1 = 10. 0 W, R 2 = 20. 0 W, R 3 = 30. 0 W, and L = 2. 00 H. Find the values of i 1 and i 2 (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. Spring 2020

PROBLEM 121 P 11 -54: In the circuit shown below , = 10 V, R 1 = 5. 0 W, R 2 = 10 W, 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 R 1, (b) the current i 2 through R 2, (c) the current i through the switch, (d) the potential difference across R 2, (e) the potential difference across L, and (f) the rate of change di 2/dt. Spring 2020

PROBLEM 121 P 11 -55 P: 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. Spring 2020