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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