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 o

Question

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 of P 2 ​ : P 1 ​ is x ​ : 1. The value of x is _____.

TestHub · Accepted Answer

The formula to calculate the power dissipated in the first case can be written as
$P_{1} = \frac{V _{0}^{2}}{R} ... (1)$
When the wire is halved, its resistance will also become half the previous value.
Thus, the formula to calculate the power dissipated in the second case can be written as
$P_{2} = \frac{V _{0}^{2}}{\frac{R}{2}} \times 2 = \frac{4 ( V _{0} ) ^{2}}{R} ... (2)$
Divide equation (2) by equation (1) to calculate the required ratio.
$\frac{P _{2}}{P _{1}} = \frac{\frac{4 ( V _{0} ) ^{2}}{R}}{\frac{( V _{0} ) ^{2}}{R}} = 4 = 16$
Hence, $x = 16$ .

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