
Concept explainers
(a)
The time taken by the current to reach
(a)

Answer to Problem 58P
The time taken by the current to reach
Explanation of Solution
Write the equation for the current in a
Here,
Write the equation for the time constant of a
Here,
Given that the value of the current is
Put equations (II) and (III) in equation (I) and rewrite the equation for
Conclusion:
Given that the value of the inductance is
Substitute
Therefore, the time taken by the current to reach
(b)
The maximum energy stored in the conductor.
(b)

Answer to Problem 58P
The maximum energy stored in the conductor is
Explanation of Solution
Write the equation for the magnetic energy stored in an inductor.
Here,
The maximum energy will be stored in the inductor when the current flowing through it is maximum.
Write the equation for the maximum current.
Here,
Put the above equation in equation (V).
Conclusion:
Given that the potential difference of the battery is
Substitute
Therefore, the maximum energy stored in the conductor is
(c)
The time taken for the energy stored in the inductor to reach
(c)

Answer to Problem 58P
The time taken for the energy stored in the inductor to reach
Explanation of Solution
According to equation (V), the energy stored is proportional to the square of the current. Apply this on equation (I) to determine the expression for the instantaneous energy stored in the inductor.
Here,
Given that the value of the energy stored is
Put the above equation in equation (VII) and rewrite it for
Put equation (II) in the above equation.
Conclusion:
Substitute
The negative root has no meaning since time is greater than or equal to zero.
The time calculated is more than the result of part (a). This is because energy stored in the inductor is proportional to the square of the current and it takes longer for the square of the current to be
Therefore, the time taken for the energy stored in the inductor to reach
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