Question

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

• A. $72\%$
• B. $91\%$
• C. $85\%$
• D. $96\%$

Answer 1

The correct option is D

$96\%$

Step 1. Given data:

The total resistance, $R=2\Omega$

The power of the electrical line, $$\begin{gathered} P=1kW \\ =1000W \end{gathered}$$

The voltage of the electrical line, $V=220volt$

Step 2. Formula used:

Power, $P=I\times VWatt$ [Where, $I$ is current]

Efficiency, $E=\frac{Poweroftheelectricalline}{Totalpower}\times 100\%$

Power loss, $Q=I^{2}RWatt$

Step 3. Finding the efficiency of the transmission line:

The current through the power line is,

$$\begin{gathered} I=\frac{P}{V} \\ I=\frac{1000W}{220V}=\frac{50}{11}A \end{gathered}$$

Power loss is $Q=I^{2}R={\left(\frac{50}{11}\right)}^2\times 2=41.322W$

Efficiency $E=\frac{1000}{1000+41.322}\times 100=96\%$

Therefore, the efficiency of the transmission line is $96\%$

Hence, option $\left(D\right)$ is correct.