Question

A transformer converts 200V a.c to 50V a.c. The secondary has 50 turns and load across it draws 300mA current. Calculate the current in the primary.

Answer 1

Hint: Here the voltage is decreased from $200V$a.c. to $50V$a.c. Hence the transformer is the step-down transformer. Therefore, the current will be maximum.

Formula used:
For any transformer, power across the coils is constant. Therefore,
${V_p}{i_p} = {V_s}{i_s}$
$ \Rightarrow \dfrac{{{V_p}}}{{{V_s}}} = \dfrac{{{i_s}}}{{{i_p}}}$\[\]
Where,
${V_p}$= voltage across the primary coil,
${V_s}$=voltage across the secondary coil,
${i_p}$= current across the primary coil,
${i_s}$= current across the secondary coil.

Complete step by step answer:
From the question, we have
${V_p} = 200V$
${V_s} = 50V$
\[{i_s} = 300mA\]
\[ \Rightarrow 300 \times {10^3}A\]
\[{i_p} = ?\]
The formula we have is, \[\dfrac{{{V_p}}}{{{V_s}}} = \dfrac{{{i_s}}}{{{i_p}}}\]. We want to find the current in the primary coil. Therefore,
\[{i_p} = \dfrac{{{i_s} \times {V_s}}}{{{V_p}}}\]
\[{i_p} = \dfrac{{300 \times {{10}^{ - 3}} \times 50}}{{200}}\]
\[{i_p} = 75 \times {10^{ - 3}}A\]
\[\therefore {i_p} = 75mA\]

Hence, current in the primary coil, \[\therefore {i_p} = 75mA\].

Additional Information:
(i) A transformer is a passive device that transforms power from one circuit to another circuit. A step-up transformer converts an AC with low voltage into an AC with high voltage. The step-down transformer converts an AC with high voltage into an AC with low voltage
(ii) In the step-up transformer voltage increases and the current decreases. In the step-down transformer, voltage decreases and the current increases.
(iii) Transformers are highly efficient devices. It has an efficiency of around $98\% $. For an ideal transformer, the efficiency $\eta $ should be 1.
$\eta = \dfrac{{\text{output power}}}{{\text{input power}}}$
$ = 1$
(iv)The transformer works on the magnetic induction principle. Magnetic induction is the process of generating electric current with a magnetic field.
(v) A changing magnetic field through a coil of wire, therefore, must induce an emf in the coil which in turn causes current to flow. This is how the current in the primary coil induces to the secondary.

Note:
In the transformer, power is the constant value across both primary and secondary coils. If the voltage decreases in the secondary than the primary, then the transformer steps down. In step down transformers, the current increases in the secondary than the primary.