Question

A wire of length L and three identical cells of negligible internal resistance are connected in series. Due to the current, the temperature of the wire is raised by $△T$ in time t. N identical cells are now connected in series with a wire of length 2L of same material and across-section. The temperature is raised by same amount $△T$ in same time t. The value of N is

• A. 6
• B. 4
• C. 8
• D. 9

Answer 1

The correct option is A 6

Case (i) $mC△T=\frac{(3V_o{)}^{2}t}{R}$

or $△T=\frac{9V_0^{2}t}{mCR}$ ...(1)

Case (ii) $2mC△T=\frac{N{V}_0{)}^{2}t}{2R}$

or $△T=\frac{N^2{V}_0^{2}t}{4mCR}$ ...(1)

Equating (1) and (2) we get, $N^2=36$ or $N=6$