Question

A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns. The output power is delivered at 230 V by the transformer. If the current in the primary of the transformer is 5A and its efficiency is $90\%$, the output current would be
(A) 25A
(B) 50A
(C) 35A
(D) 45A

Answer 1

For calculating the efficiency of a step down transformer we use following expression
$\eta = \dfrac{{{P_{out}}}}{{{P_{in}}}}$
Where power is given by
$P = IV$

Complete step by step answer:
For calculating the efficiency of a transformer, we use following expression
$\eta = \dfrac{{{P_{out}}}}{{{P_{in}}}}$ …..(1)
For a step down transformer
$(output\,power){P_{out}} = {V_S}{I_S}$ …..(2)
Where ${V_S} =$ voltage of secondary winding
${I_S} =$ Current flowing in secondary winding
and input power ${P_{in}} = {V_P}{I_P}$
Where ${V_P} =$ voltage across primary winding
${I_P} =$ Current flowing in primary winding
From equation 1, 2 and 3, we get
$\eta = \dfrac{{{V_S}{I_S}}}{{{V_P}{I_P}}}$
In question, given that ${V_P} = 2300volt$
${I_P} = 5amp$
${V_S} = 2300volt$
${I_S} = ?$
$\eta = 90\% = \dfrac{{90}}{{100}}$
$\eta = 0.9$
So, $0.9 = \dfrac{{230 \times {I_S}}}{{2300 \times 5}}$
$0.9 = \dfrac{1}{{10}} \times \dfrac{{{I_S}}}{5}$
${I_S} = 0.9 \times 50 = 45amp$

So, the correct answer is “Option D”.

Note:
In step down transformers the number of turns in primary winding is more compared to secondary winding.
In step up transformers the number of turns in secondary winding is more compared to primary winding.
The relation between voltage and number of turns used in many problems of transformer i.e., $\dfrac{{{V_S}}}{{{V_P}}} = \dfrac{{{N_S}}}{{{N_P}}} = \dfrac{{{I_P}}}{{{I_S}}}$