Problem 4: Currents of 3A and 1.5A flow through two wires. One that has potential difference of 60V across its ends and another that has potential difference of 120V across its ends. Compare the rate at which energy pass through each wire.

Solution:

Step: 1 Overview

Consumption of energy in resistors:
Since power is work done upon time. Work is done at the same rate at which energy is consumed, or we can say that Work done is equal to consumed energy. According to equation of power dissipation:

P=W/t
Since W=E
P=E/t
or E=Pt

Step: 2 Calculation

Given:

I₁=3A
I₂=1.5A
V₁=60V
V₂=120V

Required:

E₁=?
E₂=?

Solution:

Since:
P=VI
E=VIt
E₁=V₁I₁t
E₁=(60)(3)t
E₁=180t

Similarly,
E₂=V₂I₂t
E₂=(120)(1.5)t
E₂=180t

Comparsion:
E₁:E₂=180t:180t
E₁:E₂=1:1 (Ans)
hence in both cases energy consumes at the same rate.