Given below are two statements: Statement I: Maximum power is...

Given below are two statements:

Statement I: Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an $AC$ source, when resonance occurs.

Statement II: Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage.

In the light of the above statements, choose the correct answer from the options given below:

Options

AStatement $I$ is false but Statement $II$ is true
BBoth Statement $I$ and Statement $II$ are true
CStatement $I$ is true but Statement $II$ is false
DBoth Statement $I$ and Statement $II$ are false

Correct answer

B. Both Statement $I$ and Statement $II$ are true

Step-by-step solution

The formula for impedance is given by
$Z = \sqrt{{R}^{2} + {\left({X}_{L} - {X}_{C}\right)}^{2}}$
At resonance, ${X}_{L} = {X}_{C}$ . So, ${Z}_\min = R$
Power will be maximum when impedance is minimum. Thus the maximum power occurs in a purely resistive circuit.

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