In an A.C circuit, the ratio of r.m.s value to peak value of current is

Analyze the question: We need the ratio I_rms / I_peak for an alternating current (sinusoidal).

Concept: The r.m.s. (root mean square) value of an A.C. is the steady D.C. value that would produce the same heating effect in a resistor. For a sinusoidal current I = I₀ sin(ωt):

• Mean of I² over one cycle = I₀² × ½ (because the average of sin²(ωt) is ½)
• r.m.s. = √(I₀²/2) = I₀/√2

Solution:

I_rms = I₀ / √2

Ratio = I_rms / I₀ = 1/√2 ≈ 0.707

Check the other options:

• A (2) and D (√2) are greater than 1, which is impossible since the r.m.s. value can never exceed the peak value.
• B (1/2) would be the ratio if you forgot the square root.

Answer: Option C, 1/√2.

Tip: Remember "r.m.s. = 0.707 × peak". For example, Nigerian mains of 240 V r.m.s. has a peak of about 240 × √2 ≈ 339 V. Also, the ratio must always be less than 1, so you can quickly eliminate A and D.