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RMS value of a current that is a constant plus a sinusoid

The same question, asked 3 times: 2021 Paper 20*, 4 Apr 2024*, 7 Apr 2025. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 20

    22
    The alternating current is given by
    i={42sin⁡(2πTt)+10}Ai=\left\{ \sqrt{42}\sin\left( \frac{2\pi}{T}t \right)+ 10 \right\}A
    The r.m.s. value of this current is ____\_\_\_\_ A.

  2. Question 2

    4 Apr 2024

    24
    A alternating current at any instant is given by i=[6+56sin⁡(100πt+π3)]Ai =\left\lbrack 6 +\sqrt{56}\sin\left( 100\pi t +\frac{\pi}{3} \right) \right\rbrack A. The rms value of the current is _____ A.

  3. Question 3

    7 Apr 2025

    9
    An ac current is represented asi=52+10cos⁡(650πt+π6) Amp i= 5\sqrt{2}+ 10\cos\left( 650\pi t+\frac{\pi}{6} \right)\text{~Amp~}The r.m.s value of the current is.

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