A potential V_o 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 V_o is applied across the length of the each half. The total power dissipation across two wires is P₂. The ratio P₂ : P₁ is $\sqrt{x} : 1$ . The value of x is ___.

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answer is 16.

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Detailed Solution

$P_{1} = \frac{V_{0}^{2}}{R} - - - - (1)$

$P_{2} = \frac{V_{0}^{2}}{R / 2} + \frac{V_{0}^{2}}{R / 2} = \frac{4 V_{0}^{2}}{R} = 4 P_{1}$

$\frac{P_{2}}{P_{1}} = 4 = \sqrt{x} : 1$

$x = 16$

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