Question

Match the following

$\begin{array}{cc}Currents& r.ms.values\\ \left(1\right)x_{0}sin\omega t& \left(i\right)x_0\\ \left(2\right)x_{0}sin\omega tcos\omega t& \left(ii\right)\frac{x_0}{\sqrt{2}}\\ \left(3\right)x_{0}sin\omega t+x_{0}cos\omega t& \left(iii\right)\frac{x_0}{\left(2\sqrt{2}\right)}\end{array}$

• A. 1. (i), 2. (ii), 3
• B. 1. (ii), 2. (i), 3. (ii)
• C. 1. (ii), 2. (iii), 3. (i)
• D. None of these

Answer 1

The correct option is C 1. (ii), 2. (iii), 3. (i)

1. rms values$=\frac{x_0}{\sqrt{2}}$

2. $x_{0}sin\omega tcos\omega t=\frac{x_0}{2}sin2\omega t\Rightarrow$ rms value = $\frac{x_0}{2\sqrt{2}}$

3. $x_{0}sin\omega t+x_{0}cos\omega t\Rightarrow$rms value = $\sqrt{{\left(\frac{x_0}{\sqrt{2}}\right)}^2+{\left(\frac{x_0}{\sqrt{2}}\right)}^2}$

$=\sqrt{x_0^2}=x_0$