Question

A bulb with rating 250 V, 100 W is connected to a power supply of 220 V situated 10 m away using a copper wire of area of cross-section 5 mm2. How much power will be consumed by the connecting wires? Resistivity of copper = 1.7 × 10−8 Ωm

Answer 1

The connecting wires consume 8.4 mW.

Explanation:

• Consider that the bulb’s resistance is R. Bulb consumes the power P, when operated at the voltage V. Then,  

        $R=V 2 P=625 \Omega$

• The copper wire’s resistance $=\mathrm{Rc}=\rho \mathrm{lA}=0.034 \mathrm{\Omega}$

• The effective resistance is shown as $\text { Reff }=\mathrm{R}+\mathrm{Rc}=625.034 \Omega$  

• The power station supplies the current as

        I = VReff = 220625.034  A

• To the connecting wire’s one side, the power supplied is P’ = i2Rc    =220625.0342×0.034

• On both the sides, the total power is  2P’ = 220625.0342 × 0.034 × 2  =8.4 mW