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QPages 328-329: Q3: HC Verma: Concepts of Physics - Volume 2 Alternating Current Pages 328-329: Q3 Solution: Two alternating currents are given by and . Will the rms values …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often think a phase shift changes the amplitude or the rms value of a sinusoid. However, the rms of $i(t)=i_0sin(omega t+phi)$ is $i_0/sqrt2$, because squaring the signal removes the phase: $langlesin^2(omega t+phi) angle=1/2$ for any $phi$. Always remember that rms depends only on the peak magnitude, not on the phase offset.

Two alternating currents are given by

i_1 = i_0 \sin \omega t

and

i_2 = i_0 \sin\omega t + \pi/3)

. Will the rms values of the currents be equal or different?

Step-by-Step Verified Solution

**Answer:** Equal. **Step-by-Step Explanation:** The rms value of an alternating current depends only on its peak value:

I_{rms} = \frac{i_0}{\sqrt{2}}

. Both currents have the same peak value

i_0

, so their rms values are equal regardless of the phase difference [citation:14][citation:16].

All Questions in this Chapter

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