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If the rms current in a 50 Hz a.c. circuit is 5 A and at time t = 0 the current I is 0, the value of the current I at t = 1/(300) s is ______ A.

Asked in GSEB Board March 2023 · Instantaneous values and timing

• (1) 5√2
• (2) 5√3/2
• (3) 5/6
• (4) 5/(√2)

Step-by-step solution

Why the other options are wrong

• (1) This is the peak current I₀. The current reaches it only at ω t = π/2, i.e. at t = 1/(200) s; at t = 1/(300) s the phase is only π/3.
• (3) Treats the current as growing in proportion to time: 5×t/T = 5×(50)/(300) = 5/6. The current follows a sine curve, I = I₀ sin ω t, not a straight line.
• (4) Divides the given value by √2, as though 5 A were the peak and its rms value were wanted. 5 A is already the rms value, and the question asks for an instantaneous value.

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