Question

The wire have resistance R and 2R . When both are joining in series and parallel then ratio of heat generated in this situation on applying the same voltage is

Answer 1

resistance of each of the identical wires is R

a) series

Rtotal=2R

power dissipated(heat lost) = P1=V2/2R

b) parallel

Rtotal=R/2

power dissipated(heat lost) = P2=2V2/R

P1/P2=1/4

Answer 2

Explanation:

For series combination, equivalent resistance is given by :

$R_s=R+2R=3R$ .....(1)

For parallel combination, equivalent resistance is given by :

$\dfrac{1}{R_p}=\dfrac{1}{R}+\dfrac{1}{2R}\\\\R_p=\dfrac{2R}{3}$ ......(2)

As the voltage is same.

Heat generated is given by :

$H=\dfrac{V^2t}{R}$

For series combination, heat generated is:

$H_s=\dfrac{V^2t}{R_s}\\\\H_s=\dfrac{V^2t}{3R}$ .......(3)

For parallel combination, heat generated is:

$H_p=\dfrac{V^2t}{R_p}\\\\H_s=\dfrac{3V^2t}{2R}$ .....(4)

Taking ratio of equation (3) and (4) we get :

$\dfrac{H_p}{H_s}=\dfrac{2}{9}$

So, the ratio of heat generated to the parallel to the series combination is 2:9.

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