Question

2 identical resistors are first connected in series and then in parallel to a source of supply. Find the ratio of heat produced in two cases

Answer 1

Answer:

Ratio, $\dfrac{H_s}{H_p}=4$

Explanation:

Let the resistance of the identical resistor is R. In series combination, the equivalent resistance is given by :

$R_{eq}=R_1+R_2$

Here, two resistors are identical

$R_{eq}=R+R=2R$

In parallel combination, the equivalent resistance is given by :

$\dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}$

$\dfrac{1}{R_{eq}}=\dfrac{1}{R}+\dfrac{1}{R}$

$R_{eq}=\dfrac{R}{2}$

Heat produced is given by :

For series combination, $H_s=I^2(2R)t$....(1)

For parallel combination, $H_p=I^2(R/2)t$.........(2)

Dividing equation (1) and (2) as :

$\dfrac{H_s}{H_p}=4$

So, the ratio of heat produced in both cases is 4 : 1. Hence, this iss the required solution.