Question

A group of electric lamps having total power rating of $600 \,W , 200\, V$ is supplied by an $AC$ voltage $V=169 \sin \left(314 t+60^{\circ}\right)$. The rms value of the current is

• A. 10 A
• B. 9.04 A
• C. 1.48 A
• D. 8 mA

Answer 1

Answer: (C)

The general equation for the AC voltage is
$\varepsilon=\varepsilon_{0} \sin (\omega t+\theta)$
Comparing it with the given equation, we find that
$\varepsilon=V, \varepsilon_{0}=169\, V , \omega=314, \theta=60^{\circ}$
Let $\varepsilon_{ rms }$ and $I_{ rms }$ represent the rms value of $AC$ voltage and current, respectively. Clearly,
$\varepsilon_{ rms } =\frac{\varepsilon_{0}}{\sqrt{2}}=\frac{169}{\sqrt{2}} V =119.5\, V$
$P =\frac{V^{2}}{R}$
$R =\frac{V^{2}}{P}=\frac{(220)^{2}}{600}$
$i_{ rms } =\frac{119.5 \times 600}{(220)^{2}}=1.48\, A$
$\left(\because V_{ rms }=I_{ rms } R\right)$