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An electric lamp of 100 Ω, a toaster of resistance 50 Ω, and a water filter of resistance 500 Ω are connected in parallel to a 220 V source. What is the resistance of an electric iron connected to the same source that takes as much current as all three appliances, and what is the current through it?
Here, R1 = 100, R2 = 50, R3 = 500, and V = 220V
I1 = R1/V
I1 = 220/100
I2 = R2/V
I2 = 220/50
I3 = R3/V
I3 = 220/500
⇒ Total current = I1 + I2 + I3
I = 220/100 + 220/50 + 220/500
I = 220 (1/100 + 1/50 + 1/500)
I = 220 ((5 + 10 + 1)/500)
I = 220 (16/500)
I = 220 X 0.032 A
I = 7.04 A
R if iron = V/I
R = 220/7.04
R = 31.25 Ω
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