An electric lamp of 100 ?, a toaster of resistance 50 ?, and a water filter of resistance 500 ? 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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This is a classic problem to determine the equivalent resistance of a parallel arrangement of circuit elements.
Since, in parallel, the net or total current is the sum of currents through each path connected in parallel to each other,
I = I1 + I2 + I3
or, V/R = V/R1 + V/R2 + V/R3 (Since the potential difference across each element is the same as the net potential difference across the circuit)
or, 1/R = 1/R1 + 1/R2 + 1/R3
or, 1/R = 1/100 + 1/50 + 1/500
= (5 + 10 + 1)/500
= 16/500
or, R = 500/16
= 125/4 = 31 1/4 ohm
This is the required resistance for the electric iron to meet the requirements as per the problem.
Since, in parallel, the net or total current is the sum of currents through each path connected in parallel to each other,
I = I1 + I2 + I3
or, V/R = V/R1 + V/R2 + V/R3 (Since the potential difference across each element is the same as the net potential difference across the circuit)
or, 1/R = 1/R1 + 1/R2 + 1/R3
or, 1/R = 1/100 + 1/50 + 1/500
= (5 + 10 + 1)/500
= 16/500
or, R = 500/16
= 125/4 = 31 1/4 ohm
This is the required resistance for the electric iron to meet the requirements as per the problem.
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