Question

A step-down transformer reduces the voltage of the transmission line from $2200\mathrm{V}$ to $220\mathrm{V}$. The power delivered by it is $880\mathrm{W}$ and its efficiency is $88\%$. The input current is?

• A. $0.045\mathrm{A}$
• B. $4.65\mathrm{mA}$
• C. $0.45\mathrm{A}$
• D. $4.65\mathrm{A}$

Answer 1

The correct option is C

$0.45\mathrm{A}$

Step 1: Given information

Voltage reduced from $2200\mathrm{V}$ to $220\mathrm{V}$.

Output power = $880\mathrm{W}$

Efficiency percentage = $88\%$

Step 2: Formula used

$$\begin{gathered} Efficiency,\text{η=}\frac{\mathrm{Output}\mathrm{power}}{\mathrm{Input}\mathrm{power}} \\ Power,P=IV \end{gathered}$$

Step 3: Calculating input current

The efficiency of the transformer will be:

$$\begin{gathered} \text{η=}\frac{\mathrm{Output}\mathrm{power}}{\mathrm{Input}\mathrm{power}} \\ \frac{88}{100}=\frac{880}{{\mathrm{P}}_{\mathrm{i}}} \\ {\mathrm{P}}_{\mathrm{i}}=1000\mathrm{W} \end{gathered}$$

The input current is:

$$\begin{gathered} {\mathrm{I}}_{\mathrm{p}}=\frac{{\mathrm{P}}_{\mathrm{i}}}{{\mathrm{V}}_{\mathrm{i}}} \\ =\frac{1000}{2200} \\ =0.45\mathrm{A} \end{gathered}$$

Therefore, the input current will be $0.45\mathrm{A}$ that is option C is correct.