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?

Answer 1

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.