Concept explainers
The equivalent inductance for the system.
Answer to Problem 83CP
The equivalent inductance for the system is
Explanation of Solution
The flow of current in the circuit is as shown in the figure below.
Figure-(1)
Here,
Write the expression based on junction rule.
Here,
Write the expression to obtain the loop rule.
Here,
Write the expression based on junction rule to obtain the current division in the circuit.
Here,
Differentiate the above equation with respect to time
Write the expression based on loop rule to obtain the potential drop in the left loop.
Write the expression based on loop rule to obtain the potential drop in the right loop.
As the inductor
Compare equation (III) and (IV).
Further solve the above equation.
Substitute
Write the expression to obtain the voltage across the circuit.
Here,
Substitute
Further substitute
Compare equation (V) and (VI).
Further solve the above equation.
Therefore, the equivalent inductance for the system is
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Chapter 32 Solutions
Physics for Scientists and Engineers with Modern, Revised Hybrid (with Enhanced WebAssign Printed Access Card for Physics, Multi-Term Courses)
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