A transformer having efficiency of 90% is working on 200 V and 3 kW power supply. If the current in the secondary coil is 6 A, the voltage across the secondary coil and the current in the primary coil respectively are [2014]

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Solution

Q.
A transformer having efficiency of 90% is working on 200 V and 3 kW power supply. If the current in the secondary coil is 6 A, the voltage across the secondary coil and the current in the primary coil respectively are [2014]

1 300 V, 15 A

2 450 V, 15 A

3 450 V, 13.5 A

4 600 V, 15 A

Ans.
(2)

Here, Efficiency of the transformer, $η = 90 %$

Input power, $P_{in} = 3 kW = 3 \times 10^{3} W = 3000 W$

Voltage across the primary coil, $V_{p} = 200 V$

Current in the secondary coil, $I_{s} = 6 A$

As $P_{in} = I_{p} V_{p}$

$∴$ $Current in the primary coil, I_{p} = \frac{P_{in}}{V_{p}} = \frac{3000 W}{200 V} = 15 A$

Efficiency of the transformer,

$η = \frac{P_{out}}{P_{in}} = \frac{V_{s} I_{s}}{V_{p} I_{p}} ∴ \frac{90}{100} = \frac{6 V_{s}}{3000}$ or $V_{s} = \frac{90 \times 3000}{100 \times 6} = 450 V$

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