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 cross-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

Answer: (A)

6

Answer 2

Case I : mC∆T = $\frac{(3V_{0})^{2}t}{R}$ ⇒ ∆T = $\frac{9V_{0}^{2}t}{mCR}$

Case II : 2mC∆T = $\frac{(NV_{0})^{2}t}{2R}$ ⇒ ∆T = $\frac{N^{2}V_{0}^{2}t}{4mCR}$

∴ N² = 36 ⇒ N = 6