Ten identical cells connected in series are needed to heat a wire of length one meter and radius 'r' by 10 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' ?
- 20
- 30
- 40
- 10
Answer
(1) 20
Solution
Heat needed: H = ms l (same radius) ⇒ H2 = 2H1
Resistance: R l ⇒ R2 = 2R1
With n cells of emf E in series (internal resistance negligible): H = (nE)2Rt
⇒ H2H1 = n22n12 R1R2
⇒ 2 = n22100 12
⇒ n22 = 400
∴ n2 = 20
Answer: (1)