A group of electric lamps having total power rating of 600 W , 200 V is supplied by an AC voltage V=169 sin (314 t+60°). The rms value of the current is

Question

A group of electric lamps having total power rating of 600 W , 200 V is supplied by an AC voltage V=169 sin (314 t+60°). The rms value of the current is (A) 10 A (B) 9.04 A (C) 1.48 A (D) 8 mA

Tardigrade Admin · Accepted Answer

The general equation for the AC voltage is

ε = ε_{0} sin (ω t + θ)

Comparing it with the given equation, we find that

ε = V, ε_{0} = 169 V, ω = 314, θ = 6 0^{\circ}

Let

ε_{r m s}

and

I_{r m s}

represent the rms value of

A C

voltage and current, respectively. Clearly,

ε_{r m s} = \frac{ε _{0}}{2} = \frac{169}{2} V = 119.5 V

P = \frac{V ^{2}}{R}

R = \frac{V ^{2}}{P} = \frac{( 220 ) ^{2}}{600}

i_{r m s} = \frac{119.5 \times 600}{( 220 ) ^{2}} = 1.48 A

(∵ V_{r m s} = I_{r m s} R)

Q. A group of electric lamps having total power rating of 600W,200V is supplied by an AC voltage V=169sin(314t+60∘). The rms value of the current is

10 A

9.04 A

1.48 A

8 mA

Q. A group of electric lamps having total power rating of $600 W, 200 V$ is supplied by an $A C$ voltage $V = 169 sin (314 t + 6 0^{\circ})$ . The rms value of the current is