In the given circuit $R$ in pure resistance and $X$ is unknown circuit element. An AC voltage source is applied across $A$ and $C$ . If $V_{A B} = V_{A C}$ , then $X$ is

Pure resistance

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Pure inductance

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Combination of inductance and capacitance at resonance

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None of the above

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Solution

The correct option is B Combination of inductance and capacitance at resonance
Since the voltage across the resistive element is same as the voltage applied, the voltage drop across $B C$ is zero. This is possible only when the ohmic value of the element connected across $B C$ is zero. So, $X$ should be combination of inductance and capacitance at resonance.

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In the given circuit R in pure resistance and X is unknown circuit element. An AC voltage source is applied across A and C. If VAB=VAC, then X is

In the given circuit $R$ in pure resistance and $X$ is unknown circuit element. An AC voltage source is applied across $A$ and $C$ . If $V_{A B} = V_{A C}$ , then $X$ is