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Question
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?
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Solution
Resistance of electric lamp, R1 = 100 Ω
Resistance of toaster, R2 = 50 Ω
Resistance of water filter, R3 = 500 Ω
Potential difference of the source, V = 220 V
These are connected in parallel, as shown in the following figure
Let R be the equivalent resistance of the circuit.
The net resistance in parallel is given by
`1/R = 1/R_1 + 1/R_2 + 1/R_3`
Here, R1 = 100 Ω, R2 = 50 Ω and R3 = 500 Ω
`1/R = 1/100 + 1/50 + 1/500`
`= (5 + 10 + 1)/500`
= `16/500`
`R=500/16`
R = 31.25 Ω
Now, using Ohm’s law V = IR, we have
I = V/R
`=(220 V)/(31.25 Ω)`
= 7.04 A
Hence, the resistance of electric iron is 31.25 Ω and current through it is 7.04 A.
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