The switch in Figure P31.15 is open for t < 0 and is then thrown closed at time t = 0. Find (a) the current in the inductor and (b) the current in the switch as functions of time thereafter.
(a)
Answer to Problem 32.26P
Explanation of Solution
Given info: The value of resistance
Explanation:
Formula to calculate current in a loop as per Kirchhoff law is,
Here,
Write the expression for net voltage in loop 1,
Write the expression to calculate net voltage in loop 2,
Here,
Substitute
Substitute
Arrange the terms of above equation to simplify for integration.
On integrate,
Assume
Differentiate above equation,
Substitute
Substitute
Apply boundary condition,
Substitute
Substitute
Further solve the above expression.
Thus, the current in inductor in the terms of time is
Conclusion:
Therefore, the current in inductor in the terms of time is
(b)
Answer to Problem 32.26P
Explanation of Solution
Formula to calculate current in inductor, from equation (VII)
Formula to calculate current in switch, from equation, from equation (IV)
Substitute
Thus, current in switch is
Conclusion:
Therefore, the current in switch is
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Chapter 32 Solutions
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