First slide

Electrical power

Question

A wire of length L and of 3 identical cells of negligible internal resistance are connected in series. Due to the current, temperature of wire rises $Δ T$ in time t. A number of N similar cells is now connected in series with a wire of same material and cros-section but length 2 L. The temperature of wire is raised by same amount $Δ T$ in same time t. Find the value of N

Moderate

A

4
B

5
C

6
D

7

Solution

$\frac{V^{2}}{R} t = m s (Δ T) \Rightarrow \frac{V^{2} A t}{ρ L} = d A L (Δ T)$
$\Rightarrow \frac{V^{2}}{L^{2}} = \frac{d s ρ (Δ T)}{t} = constant$
$\Rightarrow \frac{{(3 E)}^{2}}{L^{2}} = \frac{{(N E)}^{2}}{{(2 L)}^{2}} \Rightarrow N^{2} = 36 \Rightarrow N = 6$

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