(a) Explanation Given Info: The resistance of the resistor is 15.0 Ω . The battery emf is 6.30 V with S 2 open and S 1 closed. After several minutes S 1 open and S 2 closed then at 2.00 ms the current decayed to 0.280 A . Sketch the given circuit as follows, Refer figure 2, the circuit switch S 2 is open and the switch S 1 is closed at a time, and the inductor acts like a short circuit for the DC Source. The initial current in the circuit is, Apply the Kirchhoff’s voltage rule for the loop of battery ( ε ) , resistor R and switch S 1 , ε − I 0 R = 0 Rearrange the equation to find I 0 , I 0 = ε R (I) ε is the battery emf in the circuit. R is the resistance of resistor. Substitute 6.30 V for ε and 15.0 Ω for R in equation (I) to find I 0 , I 0 = 6 ⋅ 30 V 15 ⋅ 0 Ω Substitute units V / A for Ω to find I 0 in amps, I 0 = 6 ⋅ 30 V 15 ⋅ 0 V / A = 0 ⋅ 42 A Refer figure 3, after several minutes the circuit switch S 1 is open and the switch S 2 is closed the circuit current is, Refer figure 3, apply the Kirchhoff’s loop equation for the loop resistor R , inductor L and switch S 2 as, R i ( t ) + L d d t i ( t ) = 0 R i ( t ) d t + L d i ( t ) = 0 d i ( t ) i ( t ) = − R L d t Take integral on both sides, R i ( t ) d t + L d i ( t ) = 0 ∫ 0 t d i ( t ) i ( t ) = ∫ 0 t ( − R L ) d t [ ln ( i ( t ) ) ] 0 t = − R L [ t ] 0 t Apply the limits as follows, ln i ( t ) − ln i ( 0 ) = − R L [ t − 0 ] ln i ( t ) i ( 0 ) = − R L t i ( t ) i ( 0 ) = e − R L t i ( t ) = i ( 0 ) e − R L t Substitute I 0 for initial current i ( 0 ) to find i ( t ) , i ( t ) = I o e − ( R L ) t Refer the equation (II) formula to calculate the decayed current in the circuit is, i = I o e − ( R L ) t (II) I o is the initial current in the circuit, R is the resistance of the resistor, L is the inductance of inductor, t is the time at circuit is 2 (b) To determine The time taken for the current to reach 1.00% of its original value after switch S 1 is opened.

University Physics with Modern Physics (14th Edition)

14th Edition

ISBN: 9780321973610

Author: Hugh D. Young, Roger A. Freedman

Publisher: PEARSON

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Question

Chapter 30, Problem 30.24E

(a)

To determine

The inductance of the coil after the switch S1 is opened.

(b)

To determine

The time taken for the current to reach 1.00% of its original value after switch S1 is opened.

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Chapter 30, Problem 30.23E

Chapter 30, Problem 30.25E

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Chapter 30 Solutions

University Physics with Modern Physics (14th Edition)

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The inductance of the coil after the switch S 1 is opened.

Solution Summary: The author explains the inductance of the coil after the switch S_1 is opened.

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The inductance of the coil after the switch S1 is opened.

The time taken for the current to reach 1.00% of its original value after switch S1 is opened.

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Chapter 30 Solutions