Question 4
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

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Solution

(c) 1:4

Heat produced in the circuit is inversely proportional to the resistance R.
Let $R_{s}$ be the equivalent resistances of the wires if connected in series and $R_{p}$ be the equivalent resistances of the wires if connected in parallel.
$R_{s} = R + R = 2 R$ and $\frac{1}{R_{p}} = \frac{1}{R} + \frac{1}{R}$
$\frac{1}{R_{p}} = \frac{2}{R}$ or $R_{p} = \frac{R}{2}$
Now, the ratio of heat produced is given by
$\frac{H_{s}}{H_{p}} = \frac{\frac{V^{2}}{R_{s}} t}{\frac{V^{2}}{R_{p}} t}$
$= \frac{R_{p}}{R_{s}}$
$= \frac{\frac{R}{2}}{2 R}$
$= \frac{1}{4}$

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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 equivalent resistance in series and parallel combinations would be:

Q. (a) Define potential difference?
(b) State joules law of heating?
(c) Two conducting wires of same material and of equal lengths and equal diameters are first connected in series and then in parallel in circuit across the same potential difference. What is the ratio of heat produced in series and parallel combination?

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