Question

The instantaneous voltage through a circuit of impedance \[10\Omega\] is V = 40sin \[(50\pi t).\] The effective value of current is ______.

Options

• \[2\sqrt{2}A\]

• \[\sqrt{2}A\]

• 2 A

• 4 A

Answer 1

The instantaneous voltage through a circuit of impedance \[10\Omega\] is V = 40sin \[(50\pi t).\] The effective value of current is \[2\sqrt{2}A\].

Explanation:

Instantaneous voltage V = 40 sin \[(\omega t)\]

\[\mathrm{V(t)=V_0=\sin{(\omega t)}}\]

\[\therefore\] Peak voltage \[V_0\] = 40V

Effective voltage \[\mathrm{V}_\mathrm{rms}\]

\[=\frac{\mathrm{V}_0}{\sqrt{2}}=\frac{40}{\sqrt{2}}=20\sqrt{2}\mathrm{V}\]

Effective Current \[\mathrm{I}_\mathrm{rms}\]

\[=\frac{\mathrm{V}_{\mathrm{ms}}}{\mathrm{Z}}=\frac{20\sqrt{2}}{10}=2\sqrt{2}\mathrm{A}\]