Question

Average Power in an RLC Series Circuit Calculate the average power delivered to the series RLC circuit with R = 307 ?, L = 1.25 H, C = 4.30 ?F, f = 60.0 Hz, and ?V_{max} = 128 V. A series circuit consisting of a resistor, an inductor, and a capacitor connected to an AC source. SOLUTION Conceptualize Consider the circuit in the figure and imagine energy being delivered to the circuit by the AC source. Review Example "Analyzing a Series RLC Circuit" to see how to calculate the needed values. Categorize We find the result by using equations developed in this section, so we categorize this example as a substitution problem. Analyze Use the equation for rms voltage and the maximum voltage from example "Analyzing a Series RLC Circuit" to find the rms voltage from the source (Give your answer in volts.): ?V_{rms} = ?V_{max} / ?2 = 90 V Similarly, find the rms current in the circuit (Give your answer in A.): I_{rms} = I_{max} / ?2 = A Use the equation for average power delivered to an RLC circuit to find the power delivered by the source (Give your answer in W.): P_{avg} = I_{rms}V_{rms} cos(?) P_{avg} = W

          Average Power in an RLC Series Circuit

Calculate the average power delivered to the series RLC circuit with R = 307 ?, L = 1.25 H, C = 4.30 ?F, f = 60.0 Hz, and ?V_{max} = 128 V.

A series circuit consisting of a resistor, an inductor, and a capacitor connected to an AC source.

SOLUTION

Conceptualize Consider the circuit in the figure and imagine energy being delivered to the circuit by the AC source. Review Example "Analyzing a Series RLC Circuit" to see how to calculate the needed values.

Categorize We find the result by using equations developed in this section, so we categorize this example as a substitution problem.

Analyze

Use the equation for rms voltage and the maximum voltage from example "Analyzing a Series RLC Circuit" to find the rms voltage from the source (Give your answer in volts.):

?V_{rms} = ?V_{max} / ?2 = 90 V

Similarly, find the rms current in the circuit (Give your answer in A.):

I_{rms} = I_{max} / ?2 = A

Use the equation for average power delivered to an RLC circuit to find the power delivered by the source (Give your answer in W.):

P_{avg} = I_{rms}V_{rms} cos(?)
P_{avg} = W

Average Power in an RLC Series Circuit

Calculate the average power delivered to the series RLC circuit with R = 307 ?, L = 1.25 H, C = 4.30 ?F, f = 60.0 Hz, and ?Vmax = 128 V.

A series circuit consisting of a resistor, an inductor, and a capacitor connected to an AC source.

SOLUTION

Conceptualize Consider the circuit in the figure and imagine energy being delivered to the circuit by the AC source. Review Example "Analyzing a Series RLC Circuit" to see how to calculate the needed values.

Categorize We find the result by using equations developed in this section, so we categorize this example as a substitution problem.

Analyze

Use the equation for rms voltage and the maximum voltage from example "Analyzing a Series RLC Circuit" to find the rms voltage from the source (Give your answer in volts.):

?Vrms = ?Vmax / ?2 = 90 V

Similarly, find the rms current in the circuit (Give your answer in A.):

Irms = Imax / ?2 = A

Use the equation for average power delivered to an RLC circuit to find the power delivered by the source (Give your answer in W.):

Pavg = IrmsVrms cos(?)
Pavg = W

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