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Concept explainers
(a)
The maximum current flows through the circuit.
(a)
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Answer to Problem 58P
The maximum current flows through the circuit is
Explanation of Solution
Write an expression for the maximum current flows through the circuit.
Here,
Conclusion:
Substitute
Thus, the maximum current flows through the circuit is
(b)
The time taken for reaching the maximum current.
(b)
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Answer to Problem 58P
The time taken for reaching the maximum current is
Explanation of Solution
Write an expression for the instantaneous current.
Here,
Rearrange equation (II) to find
Write an expression for the time constant.
Here,
Rearrange the equation (III) using equation (IV).
Conclusion:
Substitute
Thus, the time taken for reaching the maximum current is
(c)
The energy stored in the inductor and the rate at which energy is dissipated in the resistor.
(c)
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Answer to Problem 58P
The energy stored in the inductor is
Explanation of Solution
Write an expression for the energy stored in the inductor.
Here,
The current is half of the maximum current. Thus, rewrite equation (VI).
Write an expression for the rate at which energy is converted in the resistor.
The current is half of the maximum current. Thus, rewrite equation (VIII).
Conclusion:
Substitute
Substitute
Thus, the energy stored in the inductor is
(d)
The maximum current flows through the circuit and the time taken for reaching the maximum current.
(d)
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Answer to Problem 58P
The energy stored is
Explanation of Solution
Write an expression for equivalent resistance.
Here,
Write an expression for the maximum current flows through the circuit.
Write an expression for the time taken for reaching the maximum current.
Conclusion:
Substitute
Substitute
Substitute
Thus, the maximum current flows through the circuit is
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Chapter 20 Solutions
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