A potential V₀ is applied across a uniform wire of resistance R. The power dissipation is P₁. The wire is then cut into two equal halves and a potential of V₀ is applied across the length of each half. The total power dissipation across two wires is P₂. The ratio P₂: P₁ is √(x): 1. The value of x is ___________. Numerical answer type. Work it out, then open the answer.

Answer: 16. P₁ = V₀²/R. Each half has resistance R/2: P₂ = 2 × (V₀²)/(R/2) = 4P₁. P₂: P₁ = 4: 1 = √(16): 1. So x = 16.

A potential V₀ is applied across a uniform wire of resistance R. The… | JEE Main 2023 (13 Apr, Shift 1)

Q23JEE Main 2023 · 13 APR · SHIFT 1Medium

Electrical Power & Heating Effect

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 $P_2 : P_1$ is $\sqrt{x} : 1$ . The value of $x$ is ___________.

Numerical answer type. Work it out, then open the answer.

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Answer: 16

$P_1 = V_0^2/R$ .
Each half has resistance $R/2$ : $P_2 = 2 \times \dfrac{V_0^2}{R/2} = 4P_1$ .
$P_2 : P_1 = 4 : 1 = \sqrt{16} : 1$ .
So $x = 16$ .

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