Question

The alternating current is given by

i = ${\displaystyle \{\sqrt{42}\sin \left(\frac{2\pi }{\text{T}}\text{t}\right)+10\}\text{A}}$

The r.m.s. value of this current is ______ A.

Options

• 11

• 22

• 33

• 44

Answer 1

The alternating current is given by

i = ${\displaystyle \{\sqrt{42}\sin \left(\frac{2\pi }{\text{T}}\text{t}\right)+10\}\text{A}}$

The r.m.s. value of this current is 11 A.

Explanation:

${\displaystyle {\text{i}}_{\text{rms}}=\sqrt{{\text{i}}_{1\text{rms}}^2+{\text{i}}_{2\text{rms}}^2}}$

= ${\displaystyle \sqrt{{\left(\frac{\sqrt{42}}{\sqrt{2}}\right)}^2+{10}^2}}$

= ${\displaystyle \sqrt{121}}$ 

⇒ ${\displaystyle {\text{i}}_{\text{rms}}}$ = 11 A