An electrical power line, having a total resistance of $2\Omega,$ delivers $1\, kW$ at $220\, V$. The efficiency of the transmission line is approximately:

Question

In a meter bridge experiment, a resistance of $ 10 \, \Omega $ is balanced by a resistance $ X $ with a balance point at $ 40 \, \mathrm{cm} $. What is the value of $ X $?

Answer 1

To find the efficiency of the transmission line, we will follow these steps:

First, calculate the power delivered to the load. The formula for power delivered is:

P = VI

where P = 1\, kW = 1000\, W and V = 220\, V. Therefore, the current I can be calculated as:

I = \frac{P}{V} = \frac{1000}{220} \approx 4.545\, A

Next, calculate the power loss in the transmission line. The power loss P_{\text{loss}} due to the resistance can be calculated using the formula:

P_{\text{loss}} = I^2 \cdot R

Substitute the known values:

P_{\text{loss}} = (4.545)^2 \cdot 2 \approx 20.66\, W

Finally, calculate the efficiency of the transmission line using the formula:

\text{Efficiency} = \left( \frac{\text{Power Delivered to Load}}{\text{Power Delivered to Line}} \right) \times 100

where Power Delivered to Line is the sum of power delivered to the load and power loss:

\text{Power Delivered to Line} = P + P_{\text{loss}} = 1000 + 20.66 = 1020.66\, W

The efficiency is then:

\text{Efficiency} = \left( \frac{1000}{1020.66} \right) \times 100 \approx 97.97 \% \approx 96 \%

Thus, the efficiency of the transmission line is approximately 96 \%.

Answer 2