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 _____.

Step-by-step solution

The formula to calculate the power dissipated in the first case can be written as P 1 = 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 = V 0 2 R 2 × 2 =   4 V 0 2 R       . . . 2 Divide equation (2) by equation (1) to calculate the required ratio. P 2 P 1 = 4 V 0 2 R V 0 2 R = 4 = 16 Hence, x = 16 .