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

Question

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) 1: 2 (B) 2: 1 (C) 1: 4 (D) 4: 1

Tardigrade Admin · Accepted Answer

H1 = (V2t/2R) ( ∵ R' = R + R =2R) H2 = (2V2t/R) ( ∵ (1/R') = (1/R) + (1/R) = (2/R) ) ∴ (H1/2) = (1/4)

Q. 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

1 : 2

2 : 1

1 : 4

4 : 1

$H_{1} = \frac{V ^{2} t}{2 R}$ ( $∵$ R' = R + R =2R) $H_{2} = \frac{2 V ^{2} t}{R}$ $(∵ \frac{1}{R ^{'}} = \frac{1}{R} + \frac{1}{R} = \frac{2}{R})$ $∴$ $\frac{H _{1}}{_{2}} = \frac{1}{4}$

Q. 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

1 : 2

2 : 1

1 : 4

4 : 1

H1​=2RV2t​ ( ∵ R' = R + R =2R) H2​=R2V2t​ (∵R′1​=R1​+R1​=R2​) ∴ 2​H1​​=41​

$H_{1} = \frac{V ^{2} t}{2 R}$ ( $∵$ R' = R + R =2R) $H_{2} = \frac{2 V ^{2} t}{R}$ $(∵ \frac{1}{R ^{'}} = \frac{1}{R} + \frac{1}{R} = \frac{2}{R})$ $∴$ $\frac{H _{1}}{_{2}} = \frac{1}{4}$