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The output voltage of a step-down transformer is measured to be 24 V, when connected to a 12 watt light bulb. The value of the peak current is ______.

Asked in GUJCET 2025 · RMS and mean values

• (1) 2√2 A
• (2) √2 A
• (3) 2 A
• (4) 1/(√2) A

Step-by-step solution

Why the other options are wrong

• (1) Comes from inverting P=VᵣₘₛIᵣₘₛ into I=V/P=(24)/(12)=2 A and then taking the √2 step correctly: 2√2≈2.83 A. The rms current is P/V=0.5 A, not 2 A.
• (2) Comes from feeding rms numbers into the peak-value form P=1/2I₀V₀, giving I=(2×12)/(24)=1 A, and then multiplying by √2 on top of that: √2≈1.41 A. The factor 1/2 is already inside the rms values and must not be used twice.
• (3) The same inversion, V/P=(24)/(12)=2 A, stopped there: the ratio is upside down and the √2 step from rms to peak is missing as well.

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