An electric oven of resistance $125 Ω$ a toaster of resistance $50 Ω$ and an electric geyser of resistance $250 Ω$ 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 the three appliances and what is the current through it?

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Solution

To find resistance of electric iron , we have to find the equivalent resistance $1 / R = 1 / R_{1} + 1 / R_{2} + 1 / R_{3}$
this gives $1 / R = 1 / 125 + 1 / 50 + 1 / 250$
solving we get , $1 / R = 8 / 250 \Rightarrow R = 250 / 8 = 125 / 4 = 31.25 Ω$

Now for solving current , $I = V / R = 220 \times 4 / 125 = 7.04 A$

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To find resistance of electric iron , we have to find the equivalent resistance 1/R=1/R1+1/R2+1/R3this gives 1/R=1/125+1/50+1/250solving we get , 1/R=8/250⇒R=250/8=125/4=31.25ΩNow for solving current , I=V/R=220×4/125=7.04A