The electric current in the circuit is given as i = i₀(t/T). The r.m.s current for the period t = 0 to t = T i $s ________.$
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Question

The electric current in the circuit is given as i = i₀(t/T). The r.m.s current for the period t = 0 to t = T i s ________.

G1 Physics · Accepted Answer

The rms value is i(rms) = √[(1/T) ∫ from 0 to T of i² dt]. Given, i = i₀(t/T). Therefore, i² = i₀²t²/T². Hence, i(rms)² = (1/T)∫ from 0 to T [i₀²t²/T²]dt. So, i(rms)² = i₀²/T³ × [t³/3] from 0 to T = i₀²/3. Therefore, i(rms) = i₀/√3. Correct option: D.