Question

A transmission line having a total resistance of $ 0.2\Omega $ delivers $ 10\;kW $ at $ 220\;V $ to a small factory. Calculate the power loss in the line.

Answer 1

Hint: Electrical power is the rate at which work is done or energy in an electrical circuit is transformed. The rate of transmission of electrical energy per unit of time by an electrical circuit is called electrical power. Electrical energy can be either kinetic or potential energy in this context. Potential energy, which is energy stored due to the relative positions of charged particles or electrical fields, is considered in most cases. $ P $ denotes electrical power and is measured using watts.

Formula Used: We will use the following simple formula to solve the above question
 $ P = {i^2}R $
Where
 $ P $ is the electrical power
 $ i $ is the amount of current
 $ R $ is the total resistance in ohm.

Complete step by step answer:
According to the question, we have the following information,
Resistance in the power line which is used to transmit electricity, $ R = 0.2\Omega $
Power supplied to the small factory, $ P = 10kW $
Voltage of the electricity which is supplied to the factory, $ V = 220V $
Whenever an electric current passes through a material, we know that the resistance of that specific material causes the heat to lose power. And the power lost is given by the resistance product of the specific material and the square of the electric current through which the electricity is transmitted.
So, to calculate the power loss in the transmission line,
 $ P = {i^2}R $
But first we need to find out the current which is supplied to the small factory
 $ i = \dfrac{P}{V} $
 $ \Rightarrow i = \dfrac{{10 \times 1000}}{{220}} $
Hence we can calculate,
 $ \therefore i = 45.45A $
Now we will put the values of electric current and resistance in the equation of power loss
 $ P = {i^2}R $
 $ P = {45.45^2} \times 0.2 = 413.1405 $
 $ \therefore $ Power loss $ = 413.14W = 0.413kW $ .

Note:
Efficient transmission involves reducing currents by stepping up the voltage before transmission and stepping it down at the far end of a substation. Stepping up and down is performed using transformers for AC power transmission.