First slide

Transformer

Question

The ratio of turns in primary to that in secondary for a transformer is 5 : 1 and power delivered by it is 500 W. What is the current in primary coil if a current of 12.5 A is flowing in the secondary coil?

Moderate

A

62.5 A
B

2.5 A
C

6 A
D

0.4 A

Solution

The transformer in question is ideal and hence it has no power losses. This gives us
$P_{in} = P_{out}$
$\Rightarrow V_{1} I_{1} = V_{2} I_{2} \dots (i)$
$Given that P_{out} = 500 W and$
I₂ = 12.5 A.
But, P_out = V₂I₂
$\Rightarrow V_{2} = \frac{P_{2}}{I_{2}} = \frac{500}{12 .5} = 40 V$
Also, given $\frac{N_{1}}{N_{2}} = \frac{5}{1} (Turns ratio)$
For an ideal transformer, $\frac{N_{1}}{N_{2}} = \frac{V_{1}}{V_{2}}$
$\Rightarrow \frac{V_{1}}{V_{2}} = \frac{5}{1}$
$\frac{V_{1}}{40} = \frac{5}{1} (∵ V_{2} = 40 V)$
$\Rightarrow V_{1} = 200 V$
Form (i), we have
$\Rightarrow V_{1} I_{1} = V_{2} I_{2}$
$\Rightarrow I_{1} = \frac{V_{2} I_{2}}{V_{1}} = \frac{40 (12 .5)}{200} = 2 .5 A$

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