Concept explainers
(a)
The angular frequency at which power delivered to the resistor is a maximum.
(a)
Answer to Problem 79CP
The angular frequency at which power delivered to the resistor is a maximum is
Explanation of Solution
Write the expression to obtain the resonance frequency in a series
Here,
Conclusion:
Substitute
Therefore, the angular frequency at which power delivered to the resistor is a maximum is
(b)
The average power delivered at the frequency which is calculates in part (a).
(b)
Answer to Problem 79CP
The average power delivered at the frequency which is calculates in part (a) is
Explanation of Solution
Write the expression to obtain the average power delivered to the circuit at the calculated frequency.
Here,
Substitute
Conclusion:
Substitute
Therefore, the average power delivered at the frequency which is calculates in part (a) is
(c)
The two angular frequencies at which power delivered is one-half the maximum value.
(c)
Answer to Problem 79CP
The two angular frequencies at which power delivered is one-half the maximum value are
Explanation of Solution
Write the expression to obtain the average power delivered in the circuit.
Here,
Substitute
Further solve the above equation.
Case (i): when
Substitute
Write expression to obtain the quadratic equation.
Here,
Compare equation (I) and (II).
Write the expression to obtain the roots of the quadratic equation.
Substitute
Case (ii): when
Substitute
Compare equation (IV) and (II).
Substitute
Conclusion:
Substitute
Consider the positive value of
Substitute
Consider the positive value of
Therefore, the two angular frequencies at which power delivered is one-half the maximum value are
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Chapter 33 Solutions
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
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