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An electric lamp of 100Ω, a toaster of resistance 50Ω, and a water filter of resistance 500Ω 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=100Ω
Resistance of toaster, R2=50Ω
Resistance of water filter, R3=500Ω
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.
1R=1R1+1R2+1R3=1100+150+1500 = 5+10+1500 = 16500
According to Ohm’s law, V = IR
I=VR
Where,current flowing through the circuit = I
I=22050016=22016500=7.04A
7.04 A of current is drawn by all the three given appliances.
Therefore, current drawn by an electric iron connected to the same source of potential 220 V = 7.04 A
Let R’ be the resistance of the electric iron.
According to Ohm’s law, V = IR’
R=VI=2207.04=31.25Ω
Therefore, the resistance of the electric iron is 31.25Ω and the current flowing through it is 7.04 A.

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