Question

A step-down transformer transforms a supply line voltage of $2200V$ into $220V$. The primary coil has $5000$ turns. The efficiency and power transmitted by the transformer are $90\%$ and $8kW$ respectively. Then, the power supplied is

• A. $9.89kW$
• B. $8.89kW$
• C. $88.9kW$
• D. $889kW$

Answer 1

The correct option is B

$8.89kW$

Step 1: Given data assumptions.

The input voltage, $V_1=2200V$

The output voltage, $V_2=220V$

Number of the turns in the primary winding, $N_p=5000$

Output power, $P_2=8kW$

Efficiency, $\eta =90\%$

Step 2: Finding the input power.

We know that,

Efficiency, $\eta =\frac{P_2}{P_1}$

Where $P_2$ and $P_1$ is the output and input power respectively.

Now,

$90\%=\frac{8}{P_1}$

$P_1=\frac{8}{90\%}$

$P_1=\frac{8\times 100}{90}$

$P_1=8.89kW$

Hence, option B is correct. The input power is $8.89kW$