(a)
The expression for the total energy that dissipated by the resistor in one time constant.
(a)
Answer to Problem 17PQ
The expression for the total energy that dissipated by the resistor in one time constant is,
Explanation of Solution
The following figure shows the given diagram-
Figure-(1)
Here,
Write the expression for current pass through the resistor.
Here,
Write the expression for power dissipated in the resistor as function of time.
Here,
Substitute
Write the expression for energy dissipated
Substitute
Integrate the above expression between the limits
Conclusion:
Therefore, the expression for the total energy that dissipated by the resistor in one time constant is
(b)
The expression for the total charge that passes through the resistor in one time constant.
(b)
Answer to Problem 17PQ
The expression for the total charge that passes through the resistor in one time constant is,
Explanation of Solution
Write the expression for decaying current.
Write the expression for power dissipated in the resistor as function of time.
Substitute
Integrate the above expression between the limits
Conclusion:
Therefore, the expression for the total energy that dissipated by the resistor in one time constant is,
(c)
The comparison between the above two results and comment.
(c)
Answer to Problem 17PQ
The energy dissipated in the resistor when the current decays is more than the energy dissipated when the current grows in the circuit.
Explanation of Solution
Write the expression for energy growth that dissipated through the resistor.
Here,
Write the expression for energy decay that dissipated through the resistor.
Here,
Take the ratio of both equations.
Conclusion:
Substitute
Therefore, the energy dissipated in the resistor when the current decays is more than the energy dissipated when the current grows in the circuit.
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Chapter 33 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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