Question

In a transformer the output current and voltage are 4 A and 20 V respectively. If the ratio of the number of turns in the primary and secondary coil is 2:1 respectively, what is the input current and voltage?
A. 2 A and 40 V
B. 1A and 20 V
C. 4 A and 10 V
D. 8 A and 40 V

Answer 1

Use the rule for voltage in the primary and secondary coil of the transformer to calculate the voltage in the primary coil. Use conservation of energy concept to find out the power in primary and secondary coils. Then you will get the relation between voltage and current for the transformer.

Formula used:
$\dfrac{{{V_S}}}{{{V_P}}} = \dfrac{{{N_S}}}{{{N_P}}}$

Here, ${V_S}$ is the voltage in the secondary coil, ${V_P}$ is the voltage in the primary coil, ${N_S}$ is the number of turns of secondary coil and ${N_P}$ is the number of turns in the primary coil.

Complete step by step answer:
We know that the transformer is an electric device used to acquire desired voltage output. The transformer has two types: step up transformer and step down transformer. In a step up transformer, the voltage in the secondary coil is stepped up by increasing the number of turns in the secondary coil. In step down transformers, the voltage in the secondary coil is decreased by decreasing the number of turns in the secondary coil.

The transformer works on the principle of induced emf. The emf in the secondary coil is changed by changing the number of turns.

The relation between voltage in the primary coil and secondary coil is,
$\dfrac{{{V_S}}}{{{V_P}}} = \dfrac{{{N_S}}}{{{N_P}}}$

Here, ${V_S}$ is the voltage in the secondary coil, ${V_P}$ is the voltage in the primary coil, ${N_S}$ is the number of turns of secondary coil and ${N_P}$ is the number of turns in the primary coil.

The voltage in the primary coil is,
${V_P} = {V_S}\dfrac{{{N_P}}}{{{N_S}}}$

Substitute 20 V for ${V_S}$, 2 for ${N_P}$ and 1 for ${N_S}$ in the above equation.
${V_P} = \left( {20\,V} \right)\left( {\dfrac{2}{1}} \right)$
$\Rightarrow {V_P} = 40\,V$

Therefore, the voltage in the primary coil is 40 V.

In transformers, the current is inversely proportional to the voltage by power relation. Therefore, we can write,
$\dfrac{{{V_P}}}{{{V_S}}} = \dfrac{{{I_S}}}{{{I_P}}}$
$\Rightarrow {I_P} = {I_S}\dfrac{{{V_S}}}{{{V_P}}}$

Here, ${I_P}$ is the current in the primary coil.

Substitute 4 A for ${I_S}$, 40 V for ${V_P}$ and 20 V for ${V_S}$ in the above equation.
${I_P} = \left( {4\,A} \right)\left( {\dfrac{{20\,V}}{{40\,V}}} \right)$
$\Rightarrow {I_P} = 2\,A$

So, the correct answer is option (A).

Note: Do not use Ohm’s law to relate the voltage and current in transformers. In a transformer, the power in the primary coil is equal to the power in the secondary coil. We know that the power is a product of voltage and current, the current is then inversely proportional to the voltage.