(a)
The angular resonant frequency.
(a)
Answer to Problem 59P
The angular resonant frequency is
Explanation of Solution
The diagram for the RLC circuit is given figure 1:
Write the equation of resonant frequency.
Here,
Conclusion:
Substitute
Thus, the angular resonant frequency is
(b)
The value of resistance in the circuit.
(b)
Answer to Problem 59P
The value of resistance in the circuit is
Explanation of Solution
Write the equation of resistance.
Here,
Conclusion:
Substitute
Thus, the value of resistance in the circuit is
(c)
The peak voltage across the resistor, inductor and capacitor at resonant frequency.
(c)
Answer to Problem 59P
The peak voltage across the resistor, inductor and capacitor at resonant frequency are respectively
Explanation of Solution
Write the equation for the peak voltage across resistor.
Here,
Write the equation of voltage across inductor.
Here,
Write the equation of the inductive reactance.
Here,
Rewrite the expression for the peak voltage across inductor by using equation (I), (IV) and (V).
At resonant frequency, the voltage across inductor and capacitor will be same.
Write the equation for the peak voltage across capacitor.
Here,
Conclusion:
Substitute
Substitute
Substitute
Therefore, the peak voltage across the resistor, inductor and capacitor at resonant frequency are respectively
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