Four bulbs are connected as shown to a battery of EMF 220 V. The voltage and power rating of the bulbs are :
Bulb 1 : 220 V, 100 W Bulb 2 : 220 V, 50 W Bulb 3 : 440 V, 400 W Bulb 4 : 440 V, 200 W
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Choose the correct choice(s)

Options

A. The current `i_1` is 0.91 A
B. The current `i_2` is 0.46 A
C. Bulb 1 consumes power 100 W
D. Bulb 4 consumes power 50 W

Explanation

For a bulb if `V_0` is voltage rating and `p_0` is power rating. Resistance of the bulb is `r=V_0^2/P_0`
so let `r_1=220^2/100=r implies r_2=220^2/50=2r`
`implies r_3=440^2/400=r and r_4=440^2/200=2r`
So, `i=V/(r//3) =(3V)/r`
`i_1=i-V/r=(2V)/r=(2(220))/(220^2/100)=10/11=0.91A`
`i+2=i-V/(2r)=(3V)/(2r)=15/22=0.68A, P_1=V^2/r=220^2/(220^2/100)=100W` , `p_4=V^2/(2r)=50W`