Question

A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns, giving the output power at 230 V. If the current in the primary of the transformer is 5 A, and its efficiency is 90%, the output current would be:
A 20A
B 50A
C 45A
D 25A

Answer 1

Hint: Efficiency of a transformer is equal to the ratio of the power output of the secondary winding, Pout to the power input of the primary winding, Pin, $\eta = \dfrac{{{P_{out}}}}{{{P_{in}}}}$.
 Power can be written as a product of voltage and current, P=V×I.
Therefore, efficiency of the transformer is written as$\eta = \dfrac{{{V_{out}}{I_{out}}}}{{{V_{in}}{I_{in}}}}$.

Complete step by step answer:
Given, input voltage/primary voltage=2300V
Number of turns in primary winding= 400
Output voltage/secondary voltage=230V
Primary current/primary current=5A
Efficiency of the transformer=90%=0.9
We know that efficiency of a transformer is the ratio of output power to the input power.
$\eta = \dfrac{{{P_{out}}}}{{{P_{in}}}}$
Power can be written as a product of voltage and current.
Substituting the values of input voltage, input current, output current and efficiency in the equation we get,
$\eta = \dfrac{{{V_{out}}{I_{out}}}}{{{V_{in}}{I_{in}}}} = \dfrac{{230{I_{out}}}}{{2300 \times 5}}$
0.9=$\dfrac{{{I_{out}}}}{{50}}$
$I_{out}$ =0.9×50=45A
Therefore the output current would be=45A.

So, the correct answer is “Option C”.

Additional Information:
The efficiency of a transformer is reflected in power (wattage) loss between the primary (input) and secondary (output) windings.

Note:
The ratio of the primary to the secondary, the ratio of the input to the output, and the turns ratio of any given transformer will be the same as its voltage ratio. In other words for a transformer: "turns ratio = voltage ratio". This relationship is given as:$\dfrac{{{V_{out}}}}{{{V_{in}}}} = \dfrac{{{n_s}}}{{{n_p}}}$