JEE Mains · Physics · STD 12 -7. Alternating current
An alternating current is given by the equation \(i=i_{1} \sin \omega t+i_{2} \cos \omega t\). The rms current will be
- A \(\frac{1}{\sqrt{2}}\left(i_{1}^{2}+i_{2}^{2}\right)^{\frac{1}{2}}\)
- B \(\frac{1}{\sqrt{2}}\left( i _{1}+ i _{2}\right)^{2}\)
- C \(\frac{1}{2}\left( i _{1}^{2}+ i _{2}^{2}\right)^{\frac{1}{2}}\)
- D \(\frac{1}{\sqrt{2}}\left( i _{1}+ i _{2}\right)\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{\sqrt{2}}\left(i_{1}^{2}+i_{2}^{2}\right)^{\frac{1}{2}}\)
Step-by-step Solution
Detailed explanation
\(i = i _{1} \sin \omega t + i _{2} \sin (\omega t +90)\) \(i_0 =\sqrt{ i _{1}^{2}+ i _{2}^{2}}\) \(i _{ rms }=\frac{ i _{0}}{\sqrt{2}}=\frac{\sqrt{ i _{1}^{2}+ i _{2}^{2}}}{\sqrt{2}}\)
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