Match the following ( Currents r.m.s. values (1) x_ 0 ω t (i) x_ 0...

1. (x_0 \sin ($\omega$t)) : This is a pure sinusoidal function. The r.m.s. value of a sinusoidal function (A \sin ($\omega$t)) is (A / $\sqrt{2}$). So, the r.m.s. value of (x_0 \sin ($\omega$t)) is (x_0 / $\sqrt{2}$). 2. (x_0 \sin ($\omega$t) \cos ($\omega$t)) : Using the trigonometric identity (\sin (2 $\omega$t)=2 \sin ($\omega$t) \cos ($\omega$t)), this can be rewritten as ($\frac{x_0}{2} \sin ($2 $\omega$t)), which is again a sinusoidal function. The r.m.s. value will be ($\frac{x_0}{2 \sqrt{2}}$). 3. (x_0 \sin ($\omega$t)+x_0 \cos ($\omega$t)) : This is a sum of two sinusoidal functions. The r.m.s. value of such a sum can befound by using 2 r.m.s. (=$\sqrt{\left(\frac{x_0}{\sqrt{2}}\right)^2+\left(\frac{x_0}{\sqrt{2}}\right)^2}=$). Now, match the r.m.s. values: 1. (x_0 \sin ($\omega$t) → x_0 / $\sqrt{2} \rightarrow$) (ii) 2. (x_0 \sin ($\omega$t) \cos ($\omega$t) → x_0 / 2 $\sqrt{2} \rightarrow$) (iii) 3. (x_0 \sin ($\omega$t)+x_0 \cos ($\omega$t) → x_0 →) (i) The correct matching is: (c) 1 . (ii), 2. (iii), 3. (i)