A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns. The output power is delivered at 230 V by the transformer. If the current in the primary of the transformer is 5 A and its efficiency is 90%, the output current would be:

We have a power transmission line that supplies an input (primary) voltage of $$V_p = 2300 \text{ V}$$ to a step-down transformer. The number of turns on the primary winding is given as $$N_p = 4000$$. The transformer delivers an output (secondary) voltage of $$V_s = 230 \text{ V}$$.

The current in the primary circuit is stated to be $$I_p = 5 \text{ A}$$. The transformer works with an efficiency of $$\eta = 90\% = 0.90$$. Our goal is to compute the secondary (output) current $$I_s$$.

First, we recall the definition of efficiency for a transformer:

$$\eta \;=\; \dfrac{P_{\text{out}}}{P_{\text{in}}}$$

Here, $$P_{\text{in}}$$ is the input power and $$P_{\text{out}}$$ is the output power.

We now calculate the input power using the elementary electric power formula $$P = V I$$:

$$P_{\text{in}} \;=\; V_p \, I_p$$

Substituting the given values,

$$P_{\text{in}} \;=\; 2300 \text{ V} \times 5 \text{ A} \;=\; 11500 \text{ W}$$

Next, we find the output power from the efficiency relation. Rearranging the efficiency formula, we get

$$P_{\text{out}} \;=\; \eta \, P_{\text{in}}$$

Putting the numbers in,

$$P_{\text{out}} \;=\; 0.90 \times 11500 \text{ W}$$

$$P_{\text{out}} \;=\; 10350 \text{ W}$$

The transformer’s secondary voltage is already given as $$V_s = 230 \text{ V}$$. Again using the power formula on the secondary side,

$$P_{\text{out}} \;=\; V_s \, I_s$$

We solve for the unknown secondary current $$I_s$$:

$$I_s \;=\; \dfrac{P_{\text{out}}}{V_s}$$

Substituting $$P_{\text{out}} = 10350 \text{ W}$$ and $$V_s = 230 \text{ V}$$, we obtain

$$I_s \;=\; \dfrac{10350}{230} \text{ A}$$

Performing the division,

$$I_s \;=\; 45 \text{ A}$$

So, the secondary winding of the transformer delivers a current of $$45 \text{ A}$$.

Hence, the correct answer is Option D.