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The identical cells connected in series are needed to heat a wire of length one meter

The identical cells connected in series are needed to heat a wire of length one meter and radius ‘r’ by 10⁰C in time ‘t’. How many cells will be required to heat the wire of length two meter of the same radius by the same temperature in time ‘t’?

Options

(a) 10
(b) 20
(c) 30
(d) 40

Correct Answer:

20

Explanation:

Resistance is directly proportional to length of the wire. As length is doubled so mass is doubled and resistance is doubled. We have
(10 E)² / R . t = mS∆T,
Now, (nE)²t / 2R = (2m) S∆T
⇒ n²E²t / 2R = 2 . 10²E²t / R
⇒ n = 20

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