Question

Ten identical cells connected in series are needed to heat a wire of length one meter and radius ‘r’ by 10°C 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’?(a) 10(b) 20(c) 30(d) 40

Answer 1

Answer:

b) 20

Explanation:

Radius = r

Temperature = 10°C

Time = t

Let ρ be resistivity of the material of the wire and r be radius of the wire. Therefore, resistance of the wire, thus -

R = p(1)/πr²

R = P/πr²

Let ε be the emf of each cell, therefore,

First case - 10 cells each of emf ε are connected in series to heat the wire of length 1 m by ΔT(=10°C) in time.

= (10ε)²/Rt = msΔT --- 1

Second case - Let n cells each of emf ε are connected in series to heat the same u,ire of length 2 m, by the same temperature ΔT(=10°C) in time same time t.

= (nε)²t/2R = 2msΔT ---2

Dividing 2 by 1 -

= n²/200 = 2

= n² = 400

= n =20

Therefore, 20 cells will be required to heat the wire of length two meter of the same radius by the same temperature in time.