In an RLC circuit, these three elements are connected in series: a resistor of 20.0 Ω, a 35.0 mH inductor, and a 50.0 μF capacitor. The ac source of the circuit has an rms voltage of 100.0 V and an angular frequency of 1.0 × 103 rad/s. (a) Find the rms current and the rms voltage across each of the circuit elements, (b) Does the current lead or lag the source voltage? (c) Draw a phasor diagram, (d) Find the average power dissipated.
(a)
The rms current and rms voltage across each of the circuit element.
Answer to Problem 93P
The rms current across each of the circuit element is
Explanation of Solution
Write the expression for capacitive reactance.
Here,
Write the expression for inductive reactance.
Here,
Write the expression for impedance.
Here,
Write the expression for rms current.
Write the expression for rms voltage across resistor.
Write the expression for rms voltage across inductor.
Write the expression for rms voltage across capacitor.
Conclusion:
Substitute,
Substitute,
Substitute,
Substitute,
Substitute,
Substitute,
Substitute,
Therefore, the average current through the coil during rotation is
(b)
Whether the current lead or lag voltage.
Answer to Problem 93P
Current lags voltage.
Explanation of Solution
The value of inductive reactance is
Conclusion:
Therefore, Current lags voltage.
(c)
Sketch the phasor diagram.
Answer to Problem 93P
The phasor diagram is shown below.
Explanation of Solution
Write the expression for phase angle.
Conclusion:
Substitute,
Therefore, the phasor diagram is.
(d)
The average power dissipated.
Answer to Problem 93P
The average power dissipated is
Explanation of Solution
Write the expression for power dissipated.
Conclusion:
Substitute,
Therefore, the average power dissipated is
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