(a)
The angular frequency at which the power delivered to the resistor is maximum.
(a)
Answer to Problem 33.79CP
The angular frequency at which the power delivered to the resistor is maximum is
Explanation of Solution
Given info: The maximum value of voltage is
For the condition of maximum power through the resistor, the current through the resistor is to be greatest. For maximum value of the current the value of impedance of the circuit has to be least. The value of impedance is least at resonance frequency.
The expression for the resonance angular frequency is,
Here,
Substitute
Conclusion:
Therefore, the angular frequency at which the power delivered to the resistor is maximum is
(b)
The average power delivered at resonance frequency.
(b)
Answer to Problem 33.79CP
The average power delivered at resonance frequency is
Explanation of Solution
Given info: The maximum value of voltage is
The expression for power delivered is,
Here,
For the condition of resonance the value of impedance is equal to the value of resistance.
Substitute
Substitute
Conclusion:
Therefore, the average power delivered at resonance frequency is
(c)
The two angular frequencies at which power is one half of the maximum value.
(c)
Answer to Problem 33.79CP
The two angular frequencies at which power is one half of the maximum value are
Explanation of Solution
Given info: The maximum value of voltage is
The expression for inductive reactance is,
Here,
The expression for capacitive reactance is,
Here,
The expression for the impedance of the circuit is.
The power is half of the maximum power.
The expression of power in terms of max power is
Substitute
Substitute
Substitute
The first values of
Substitute
The value of the angular frequency is always positive, therefore the negative value is neglected
The first values of
Substitute
The second values of
Substitute
The value of the angular frequency is always positive, therefore the negative value is neglected
The second value of
Conclusion:
Therefore, the two angular frequencies at which power is one half of the maximum value are
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Chapter 33 Solutions
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