MHT CET · Physics · Alternating Current

The primary and secondary voltage of an ideal step-down transformer is \(200 \mathrm{~V}\) and \(25 \mathrm{~V}\) respectively. The secondary is connected to a device, which draws a current of \(2 \mathrm{~A}\). The current in the primary is

A \(25 \mathrm{~mA}\)
B \(42 \mathrm{~mA}\)
C \(160 \mathrm{~mA}\)
D \(250 \mathrm{~mA}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(250 \mathrm{~mA}\)

Step-by-step Solution

Detailed explanation

For a lossless transformer, with primary coil \(\left(I_P, V_P\right)\) and secondary coil \(\left(I_S, V_S\right)\), there has to be conservation of energy per unit time:
\(\begin{aligned} & I_P V_P=I_S V_S \\ & \Rightarrow \frac{I_P}{I_S}=\frac{V_S}{V_P} \\ & \therefore \frac{I_P}{2}=\frac{25}{500} \\ & \therefore I_P=\frac{1}{4} \mathrm{~A}=250 \mathrm{~mA}\end{aligned}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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