Explanation Given data: Refer to Figure 16.92 in the textbook. The voltage source is, v ( t ) = 120 e − 3 t u ( t ) V (1) Formula used: Write an expression to calculate the value of step input. u ( t ) = { 0 t < 0 1 t > 0 Write a general expression to calculate the impedance of a resistor in s -domain. Z R = R (2) Here, R is the value of resistance of the resistor. Write a general expression to calculate the impedance of an inductor in s -domain. Z L = s L (3) Here, L is the value of inductance of the inductor. Calculation: Take Laplace transform of equation (1). V ( s ) = 120 s + 3 { ∵ L [ e − a t u ( t ) ] = 1 s + a } Using equation (2) and (3), the given circuit is redrawn as shown in Figure 1 in s -domain and use the model for mutually coupled circuit. Apply Kirchhoff’s voltage law to the loop current I 1 in Figure 1. 2 s I 1 + s I 2 + 1 ( I 1 − I 2 ) = 120 s + 3 ( 2 s + 1 ) I 1 + ( s − 1 ) I 2 = 120 s + 3 (4) Apply Kirchhoff’s voltage law to the loop current I 2 in Figure 1. s I 1 + 2 s I 2 + 1 ( I 2 − I 1 ) + 1 I 2 = 0 ( s − 1 ) I 1 + ( 2 s + 2 ) I 2 = 0 (5) Rearrange the equation (5) as follows, ( 2 s + 2 ) I 2 = − ( s − 1 ) I 1 I 2 = − ( s − 1 2 s + 2 ) I 1 (6) Substitute equation (6) in equation (4) to find the current I 1

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Chapter 16, Problem 69P

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Find the expression of current I1(s) and I2(s) in the circuit of Figure 16.92.

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Chapter 16, Problem 68P

Chapter 16, Problem 70P

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Find the expression of current I 1 ( s ) and I 2 ( s ) in the circuit of Figure 16.92.

Solution Summary: The author explains how to calculate the expression of current I_1(s) in the circuit of Figure 16.92.

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Find the expression of current I1(s) and I2(s) in the circuit of Figure 16.92.

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