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MCQEasyJEE 2024AC Generator & Transformer

JEE Physics 2024 Question with Solution

The primary side of a transformer is connected to 230 V230 \, \text{V}, 50 Hz50 \, \text{Hz} supply with a turns ratio of 10:110:1. Load resistance is 46 Ω46 \, \Omega. The power consumed is:

  • A

    12.5 W12.5 \, \text{W}

  • B

    10 W10 \, \text{W}

  • C

    11.5 W11.5 \, \text{W}

  • D

    12 W12 \, \text{W}

Answer

Correct answer:C

Step-by-step solution

Standard Method

Given: Primary voltage is 230 V230 \, \text{V}, turns ratio is N1N2=10\frac{N_1}{N_2} = 10, and load resistance is 46 Ω46 \, \Omega.

Find: Power consumed by the load resistance on the secondary side.

Use the transformer relation:

V1V2=N1N2=10\frac{V_1}{V_2} = \frac{N_1}{N_2} = 10

So,

V2=23010=23 VV_2 = \frac{230}{10} = 23 \, \text{V}

Now apply Ohm's law for the secondary current:

I2=V2R=2346=0.5 AI_2 = \frac{V_2}{R} = \frac{23}{46} = 0.5 \, \text{A}

Power consumed in the load is:

P=I22R=(0.5)2×46=11.5 WP = I_2^2 R = (0.5)^2 \times 46 = 11.5 \, \text{W}

Therefore, the power consumed is 11.5 W11.5 \, \text{W}. The correct option is C.

From the alternate form,

P=V22R=23246=11.5 WP = \frac{V_2^2}{R} = \frac{23^2}{46} = 11.5 \, \text{W}

which confirms the same result.

Direct Power Formula

Given: V1=230 VV_1 = 230 \, \text{V}, N1N2=10\frac{N_1}{N_2} = 10, R=46 ΩR = 46 \, \Omega.

Find: Load power.

First find the secondary voltage using the turns ratio:

V2=23010=23 VV_2 = \frac{230}{10} = 23 \, \text{V}

Then use the direct relation for a resistor:

P=V22R=23246=11.5 WP = \frac{V_2^2}{R} = \frac{23^2}{46} = 11.5 \, \text{W}

This works because for a pure resistance, power can be written directly as P=V2RP = \frac{V^2}{R}. Hence, the correct option is C.

Common mistakes

  • Using the turns ratio in the wrong direction is a common mistake. Here N1N2=10\frac{N_1}{N_2} = 10 means the secondary voltage is smaller, so V2=V110V_2 = \frac{V_1}{10}, not 10V110V_1.

  • Calculating power with the primary voltage instead of the secondary voltage gives an incorrect result. The load resistance is connected on the secondary side, so use V2V_2 across 46 Ω46 \, \Omega.

  • Confusing the formulas P=VIP = VI, P=I2RP = I^2R, and P=V2RP = \frac{V^2}{R} can lead to errors. For a resistor, any of these is valid only when VV and II correspond to the same side of the transformer.

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