Secondary Circuit Resistance of an Ideal Transformer

Q: Do we need the primary voltage 12kV anywhere in the calculation?

No, because both the secondary voltage (120V) and secondary power (60kW) are directly provided, fully specifying the secondary circuit.

An ideal transformer with purely resistive load operates at 12kV on the primary side. It supplies electrical energy to a number of nearby houses at 120V. The average rate of energy consumption in the houses served by the transformer is 60kW. The value of resistive load (Rs) required in the secondary circuit will be _______ mΩ.

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Question type: Numerical
Exam relevance: JEE Main · Physics
Academic status: Answer verified against the official NTA key
Source: Previous-year question
Editorial review: 19 September 2026

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Do we need the primary voltage

12 kV

anywhere in the calculation?

No, because both the secondary voltage ( $120 V$ ) and secondary power ( $60 kW$ ) are directly provided, fully specifying the secondary circuit.

Answer

Accepted answer: 240 mΩ

The value of the resistive load in the secondary circuit is 240 mΩ.

Why each option works or fails

Step-by-step solution

Given: Primary voltage $V_{p} = 12 kV = 12000 V$ , secondary voltage $V_{s} = 120 V$ , secondary average power consumed $P_{s} = 60 kW = 60000 W$ .
Find: Secondary load resistance $R_{s}$ in $m Ω$ .
Visualise: An ideal step-down transformer steps down voltage from $12 kV$ to $120 V$ . The secondary side powers resistive loads dissipating a total power of $60 kW$ .
Strategise: Since the load is purely resistive, the power dissipated is related to secondary voltage by $P_{s} = \frac{V_{s}^{2}}{R_{s}}$ , hence $R_{s} = \frac{V_{s}^{2}}{P_{s}}$ . Alternatively, compute $I_{s} = \frac{P_{s}}{V_{s}}$ and then $R_{s} = \frac{V_{s}}{I_{s}}$ .
Execute: Calculate $R_{s} = \frac{(120)^{2}}{60000} = \frac{14400}{60000} = 0.24 Ω = 240 m Ω$ .
Verify: $I_{s} = \frac{60000}{120} = 500 A$ . Then $P = I_{s}^{2} R_{s} = (500)^{2} \times 0.24 = 250000 \times 0.24 = 60000 W = 60 kW$ . The result is consistent and in $m Ω$ .

Secondary Circuit Resistance of an Ideal Transformer

What feels right?

The value of the resistive load in the secondary circuit is 240 mΩ.

Why each option works or fails

Solution

01Given

02Find

03Visualise

04Strategise

05Execute

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01Given

02Find

03Visualise

04Strategise

05Execute

✓Verify

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