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Question

Question: Two heater wires of equal length are first connected in series and then in parallel. The ratio of he...

Two heater wires of equal length are first connected in series and then in parallel. The ratio of heat produced in the two cases is

A

2 : 1

B

1 : 2

C

4 : 1

D

1 : 4

Answer

1 : 4

Explanation

Solution

Power consumed means heat produced. For constant potential difference Pconsumed=Heat1ReqP_{\text{consumed}} = \text{Heat} \propto \frac{1}{R_{eq}}

H1H2=R2R1=R/22R=14\therefore\frac{H_{1}}{H_{2}} = \frac{R_{2}}{R_{1}} = \frac{R/2}{2R} = \frac{1}{4}

(Since R2=R.RR+R=R2R_{2} = \frac{R.R}{R + R} = \frac{R}{2}and R1=R+R=2R)R_{1} = R + R = 2R)