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Question

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


A
1:2
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B
2:1
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C
1:4
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D
4:1
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Solution

The correct option is D 1:4
Since the two wires have same material, length and diameter, they have the same resistance. Let the resistance of each wire be R.
Let applied potential difference be $$V$$.

$$R_{series}=R_1+R_2$$
             $$=R+R=2R$$
$$P_{series} = V^2 / R_{series}$$
             $$=V^2/(2R)\quad ..........(i)$$

$$\cfrac{1}{R_{parallel}} = \cfrac{1}{R_1}+\cfrac{1}{R_2}$$
$$R_{parallel}=R/2$$

$$P_{parallel} = V^2 / R_{parallel}$$
              $$=2V^2/R\quad ............(ii)$$

Dividing (ii) from (i),
$$\dfrac{P_{series}}{P_{parallel}} = 1/4$$

Science
NCERT
Standard X

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