Question

Average power consumed in an A.C. series circuit is given by (symbols have their usual meaning).

• A. $E_{rms}{I}_{rms}cos\varphi$
• B. $(I_{rms}{)}^{2}R$
• C. $\frac{E_0^2}{2(|z|{)}^2}$
• D. $\frac{I_0^2|z|cos\varphi }{2}$

Answer 1

Answer: (B)

$(I_{rms}{)}^{2}R$

Let the ac circuit is a series resonant circuit.

The impedance is given as,

$Z=\sqrt{R^2+{\left(X_L-X_C\right)}^2}$

The average power is given as,

$P_{avg}=\frac{{E_{rms}}^{2}R}{Z^2}$

$P_{avg}=\frac{{E_{rms}}^{2}R}{R^2+{\left(X_L-X_C\right)}^2}$

$P_{avg}={I_{rms}}^{2}R$

Thus, the average power is ${I_{rms}}^{2}R$.