Question

In a transformer the output current and voltage are respectively $4\;{\rm{A}}$ and $20\;{\rm{V}}$. 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. 1 A and 20 V
C. 4 A and 10 V
D. 8 A and 40 V

Answer 1

The above problem can be resolved using the concepts and the fundamentals of the transformers. The mathematical relation of the ratio of the input and output voltage with the number of turns in the secondary and primary coils is used to obtain the required result. Similarly, the number of turns with the secondary and the primary coils is related to the input and the output magnitude of current.

Complete step by step answer:
Given:
The output current is given as, ${I_o} = 4\;{\rm{A}}$.
The output voltage is, ${V_o} = 20\;{\rm{V}}$.
The ratio of number of turns in the primary and second is, ${N_P}/{N_s} = 2:1$.
Write the relation for the input current is given as,
${I_i} = \left( {\dfrac{{{N_s}}}{{{N_p}}}} \right) \times {I_o}$
Solve by substituting the values as,

{I_i} = \left( {\dfrac{{{N_s}}}{{{N_p}}}} \right) \times {I_o}\\\ {I_i} = \left( {\dfrac{1}{2}} \right) \times 4\;{\rm{A}}\\\ {I_i} = 2\;{\rm{A}} \end{array}$$ Similarly, the input voltage is, $$\begin{array}{l} {V_i} = \left( {\dfrac{{{N_P}}}{{{N_S}}}} \right) \times {V_o}\\\ {V_i} = \left( {\dfrac{2}{1}} \right) \times 20\;{\rm{V}}\\\ {{\rm{V}}_i} = 40\;{\rm{V}} \end{array}$$ Therefore, the input current and voltage are 2 A and 40 V respectively **So, the correct answer is “Option A”.** **Note:** To resolve the problem, one must understand the meaning of the term transformer. The transformer is an electrical setup used to bring out the voltage variation; if the voltage is increased, then the transformer used for the purpose is known as the step-up transformer. And if the voltage is reduced, then the transformer used for the purpose is known as the step-down transformer. The transformers possess a variety of applications in various commercial sites. Moreover, the transformers use multiple variables in their analysis, like voltage and current, the phase difference, and many more that need to be understood.