Question

$\frac{2.5}{\pi} \mu F$ capacitor and $3000$ ohm resistor are joined in series to an AC source of $200$ volt and $50\, sec ^{-1}$ frequency. The power factor of the circuit and the power dissipated in it will respectively be

• A. 0.6,0.06 W
• B. 0.06,0.6 W
• C. 0.6,4.8 W
• D. 4.8,0.6 W

Answer 1

Answer: (C)

$Z=\sqrt{R^{2}+\left(\frac{1}{2 \pi v C}\right)^{2}}$
$=\sqrt{(3000)^{2}+\frac{1}{\left(2 \pi \times 50 \times \frac{2.5}{\pi} \times 10^{-6}\right)^{2}}}$
$Z=\sqrt{(3000)^{2}+(4000)^{2}}=5 \times 10^{3}\, \Omega$
So, power factor, $\cos \phi=\frac{R}{Z}=\frac{3000}{5 \times 10^{3}}=0.6$
Now, $P=V_{ mm } i_{ ms } \cos \phi=\frac{V_{ ms }^{2} \cos \phi}{Z}$
$\Rightarrow P=\frac{(200)^{2} \times 0.6}{5 \times 10^{3}}=4.8\, W$