A radio tuner has a resistance of 1.00 $\mu$$\varOmega$,a capacitance of 25.0 nF,and an inductance of 3.00 mH.If the power in the circuit is 3.9 W and it is at the resonance frequency,what is the rms voltage of the signal produced across the antenna?
A)2.21 mV
B)1.00 mV
C)1.67 mV
D)1.50 mV
E)1.97 mV

Question

Quizplus · Accepted Answer

At resonance in an LC circuit, the impedance is purely resistive, and the power can be calculated using $P = \frac{V_{rms}^2}{R}$. Rearranging for $V_{rms}$, we get $V_{rms} = \sqrt{P \cdot R}$. Substituting $P = 3.9\,W$ and $R = 1\,\Omega$, we find $V_{rms} = \sqrt{3.9 \cdot 1} = \sqrt{3.9} \approx 1.97\,V$, not mV. The correct unit should be volts (V), indicating a misunderstanding in the question's choices.

A Radio Tuner Has a Resistance of 1 μ\muμ Ω\varOmegaΩ ,A Capacitance of 25

A Radio Tuner Has a Resistance of 1 $\mu$ $\varOmega$ ,A Capacitance of 25