Chapter 3: Electricity

Q&A -Ask Doubts and Get Answers

Q
Electricity

Question:

Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then parallel in a circuit across the same potential difference. The ratio of heat produced in series and parallel combinations would be –

(a) 1:2    (b) 2:1     (c) 1:4     (d) 4:1

Answer:

It is given that two conducting wire is of the same material having equal lengths and diameters, so the resistance of wires will be the same (say) $R$.

We know,

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

It is given that both combinations are connected across the same potential so $V$ is the same for both combinations.

The ratio of heat produced in series $H_S$ to the heat produce in parallel $H_P$ is given by,

$\frac{H_S}{H_P} = \frac{\frac{V^2 t}{R_S}}{\frac{V^2 t}{R_P}}$

$\frac{H_S}{H_P} = \frac{R_P}{R_S} -------(1)$

Now, $R_S = R + R = 2R$

And, $\frac{1}{R_P} = \frac{1}{R} + \frac{1}{R}$

$\frac{1}{R_P} = \frac{1 + 1}{R}$

$\frac{1}{R_P} = \frac{2}{R}$

$R_P = \frac{R}{2}$

By putting values of $R_P$ and $R_S$ in equation (1), we get

$\frac{H_S}{H_P} = \frac{\frac{R}{2}}{2R}$

$\frac{H_S}{H_P} = \frac{1}{4}$

So, the correct option is (c).

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