Question

For a transformer, the turn ratio $3$ and its efficiency is $0.75$. The current flowing in the primary coil is $2 A$ and the voltage applied to it is $100 V$. Then the voltage and current flowing in the secondary coil are __ respectively.
(A) $150 V, 1.5 A$
(B) $300 V, 0.5 A$
(C) $300 V, 1.5 A$
(D) $150 V, 0.5 A$

Answer 1

Hint
The turn ratio is the ratio of either number of turns of secondary coil to primary coil or voltage of secondary coil to primary coil of the transformer. The efficiency of the transformer is the ratio of power of secondary coil to primary coil of the transformer.

Complete step by step answer
The turn ratio of transformer is $r=3$, the efficiency of the transformer is $\eta = 0.75$, the current in the primary coil of transformer is ${I_1} = 2\;{\text{A}}$and the voltage in the primary coil of transformer is ${V_1} = 100\;{\text{V}}$.
Use the expression of the turn ratio of the transformer to find the voltage of the secondary coil of the transformer. The expression is given as,
$r = \dfrac{{{V_2}}}{{{V_1}}}$
${V_2} = r \cdot {V_1}......\left( 1 \right)$
Substitute $3$ for $r$ and $100\;{\text{V}}$ for ${V_1}$ in the equation (1) to find the voltage of the secondary transformer.
${V_2} = \left( 3 \right)\left( {100\;{\text{V}}} \right)$
${V_2} = 300\;{\text{V}}$
Use the expression of efficiency of the transformer to find the current in the secondary coil of the transformer. The expression is given as,
$\eta = \dfrac{{{V_2} \cdot {I_2}}}{{{V_1} \cdot {I_1}}}$
${I_2} = \dfrac{{\eta \cdot {V_1} \cdot {I_1}}}{{{V_2}}}\;......\;\left( 2 \right)$
Substitute $0.75$ for $\eta$, $100 V$ for ${V_1}$, $2 A$ for ${I_1}$and $300 V$ for ${V_2}$in the equation (2) to find the current flowing in the secondary coil of the transformer.
${I_2} = \dfrac{{\left( {0.75} \right)\left( {100\;{\text{V}}} \right)\left( {2\;{\text{A}}} \right)}}{{300\;{\text{A}}}}$
${I_2} = 0.5\;{\text{A}}$
Therefore, the voltage of the secondary coil is $300 V$ and current flowing in the secondary coil is $0.5 A$ of the transformer.
Option (B) is correct.

Note
Be careful in using the expression of the turn ratio and efficiency because there is confusion in that the turn ratio is the ratio of the number of turns of primary to secondary or secondary to primary.