Question

We have a heavy power cable which is 1 foot in diameter with resistance 0.05 u 12 per foot. Connect the cable to a voltage source of 115 V. How long is the cable over which the power loss through the resistance of the cable will reach 10^10 watts?

Answer 1

Answer:

n = 26.5 ft

Explanation:

given,

diameter = 1 ft

resistance, R = 0.05 μΩ/ft

Voltage, V = 115 V

Power, P = 10¹⁰ W

Length = ?

Power through the cable

P = I² R

P = (V/R)^2 x R

$P =\dfrac{V^2}{R}$

$R = \dfrac{V^2}{P}$

$R = \dfrac{115^2}{10^{10}}$

R = 1.325 x 10⁻⁶ Ω

Length of cable in foots,

$R = n \times R_{foot}$

$1.325\times 10^{-6} = n\times 0.05 \times 10^{-6}$

n = 26.5 ft

Length of the cable is equal to n = 26.5 ft