Question

A transformer has turns ratio, $\frac{N_S}{N_P}=4$. A $200\text{V}$ AC voltage is applied across its primary coil, carrying a current of $1\text{A}$. Find the current in the circuit, connected to the secondary coil, if the transformer is $80\%$ efficient.

• A. $0.2\text{A}$
• B. $0.4\text{A}$
• C. $0.8\text{A}$
• D. $0.6\text{A}$

Answer 1

The correct option is A $0.2\text{A}$

Power supplied to the primary coil,

$P_{\text{input}}=E_P{i}_P=200\times 1=200\text{W}$

Also, efficiency,

$\eta =\frac{P_{\text{output}}}{P_{\text{input}}}$

The transformer is $80\%$ efficient.

$\Rightarrow P_{\text{output}}=0.8\times P_{\text{input}}=0.8\times 200=160\text{W}$

Further, $\frac{N_S}{N_P}=\frac{E_S}{E_P}$

$\Rightarrow E_S=E_P\times \frac{N_S}{N_P}=200\times 4=800\text{V}$

And,

$P_{\text{output}}=E_S{i}_S$

$\Rightarrow i_S=\frac{P_{\text{output}}}{E_S}$

$\Rightarrow i_S=\frac{160}{800}=0.2\text{A}$

Hence, option $\left(A\right)$ is the correct answer.