Question

An electrical device drawn 2 kW power from ac mains voltage k223 V (rms). The current differs lags in phase by $\varphi = \tan^{- 1}\left( - \frac{3}{4} \right)$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$\Omega$

Answer 2

: Here, P = 2 kW= 2×$10^{3}$W

$V_{rms} = 223V,\tan\varphi = - \frac{3}{4}$

As, $P = \frac{{V^{2}}_{rms}}{Z}$

$\Rightarrow Z = \frac{{V^{2}}_{rms}}{P} = \frac{(223)^{2}}{2000} = \frac{49729}{2000} = 24.86\Omega$

or, Z ≈ $25\Omega$

$\tan\varphi = \frac{X_{C} - X_{L}}{R} = - \frac{3}{4}$

$\therefore X_{C} - X_{L} = - \frac{3}{4}R.$

As, $Z^{2} = R^{2} + (X_{C} - X_{L})^{2}$

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

$625 = R^{2} + \frac{9}{16}R^{2} = \frac{25R^{2}}{16}$

$R^{2} = \frac{625 \times 16}{25} = 400$

$R = 20\Omega$