JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Current Electricity

A potential

V_{0}

is applied across a uniform wire of resistance R. The power dissipation is

P_{1}

. The wire is then cut into two equal halves and a potential of

V_{0}

is applied across the length of each half. The total power dissipation across two wires is

P_{2}

. The ratio

P_{2} : P_{1}

x : 1

. The value of

x

is ______.

Answer: 16

Solution

Initially, power dissipation:

P_{1} = \frac{V _{0}^{2}}{R}

When the wire is cut into two equal halves, each half has resistance

R^{'} = \frac{R}{2}

.

When

V_{0}

is applied across each half, the power dissipation in each is:

P = \frac{V _{0}^{2}}{R /2} = \frac{2 V _{0}^{2}}{R}

Total power in both halves:

P_{2} = 2 \times \frac{2 V _{0}^{2}}{R} = \frac{4 V _{0}^{2}}{R}

Therefore:

\frac{P _{2}}{P _{1}} = \frac{4 V _{0}^{2} / R}{V _{0}^{2} / R} = 4 = \frac{x}{1}

Squaring:

x = 16

JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Integer answer