Question

An electrical device draws $2kW$ power from ac mains voltage $223V\left(rms\right).$ The current differs lags in phase by $\varphi =ta{n}^{-1}(-\frac{3}{4})$ as compared to voltage. The resistance R in the circuit is:

• A. $15\Omega$
• B. $20\Omega$
• C. $25\Omega$
• D. $30\Omega$

Answer 1

Answer: (B)

$20\Omega$

Here, $P=2kW=2\times {10}^{3}W$
$V_{rms}=233V,tan\varphi =-\frac{3}{4}$
$As,P=\frac{V_{rms}^2}{Z}$

$\Rightarrow Z=\frac{V_{rms}^2}{P}=\frac{(223{)}^2}{2000}=\frac{49729}{2000}=24.86\Omega orZ=25\Omega$

$\tan \varphi =\frac{X_C-X_L}{R}=-\frac{3}{4}\therefore X_C-X_L=-\frac{3}{4}R.$

AS, $Z^2=R^2+(X_C-X_L{)}^2$

$\therefore (25{)}^2=R^2+{(-\frac{3}{4}R)}^2$

$625=\frac{25R^2}{16}.$

$R^2=\frac{625\times 16}{25}\Rightarrow R=20\Omega$