In the circuit shown, an alternating voltage source is connected to a resistor, an inductor, and a capacitor in series. The readings of the ideal voltmeters V_1 , V_2 , and V_3 connected across the resistor, inductor

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Correct answer: C. 10\

The readings of the AC voltmeters give the RMS voltage across the respective components.

V_R = 16\text{ V}

V_L = 24\text{ V}

V_C = 12\text{ V}

The total RMS voltage of the source is:

V_{\text{rms}} = \sqrt{V_R^2 + (V_L - V_C)^2}

V_{\text{rms}} = \sqrt{16^2 + (24 - 12)^2} = \sqrt{16^2 + 12^2} = 20\text{ V}

The amplitude of the current is

I_0 = 2\sqrt{2}\text{ A}

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The RMS current is:

I_{\text{rms}} = \dfrac{I_0}{\sqrt{2}} = \dfrac{2\sqrt{2}}{\sqrt{2}} = 2\text{ A}

The impedance of the circuit is:

Z = \dfrac{V_{\text{rms}}}{I_{\text{rms}}} = \dfrac{20}{2} = 10\ \Omega

Answer:

10\ \Omega

In the circuit shown, an alternating voltage source is connected to...

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