JEE Mains · Physics · STD 12 -7. Alternating current
The electric current in the circuit is given as \(i=i_{ o }(t / T)\). The r.m.s current for the period \(t=0\) to \(t=T\) is ___________
- A \(\frac{i_{0}}{\sqrt{2}}\)
- B \(i_{0}\)
- C \(\frac{i_{0}}{\sqrt{6}}\)
- D \(\frac{i_{0}}{\sqrt{3}}\)
Answer & Solution
Correct Answer
(D) \(\frac{i_{0}}{\sqrt{3}}\)
Step-by-step Solution
Detailed explanation
\(i _{ rms }^2=\frac{\int_0^{ T }\left( i _0^2 t ^2 / T ^2\right) dt }{\int_0^{ T } dt }=\frac{ i _0^2}{T^3} \cdot \frac{T^3}{3}=\frac{ i _0^2}{3}\) \(i _{ rms }=\frac{ i _0}{\sqrt{3}}\)
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