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An ac voltage \(\mathrm{v}=\mathrm{v}_0\) sin \(\omega \mathrm{t}\) is applied to a series combination of a resistor \(R…

Q1

An ac voltage \(\mathrm{v}=\mathrm{v}_0\) sin \(\omega \mathrm{t}\) is applied to a series combination of a resistor \(R\) and an element \(X\). The instantaneous current in the circuit is \(\mathrm{I}=\mathrm{I}_0 \sin \left(\omega \mathrm{t}+\frac{\pi}{4}\right)\). Then which of the following is correct ?

a

\(\mathrm{X}\) is a capacitor and \(\mathrm{X}_{\mathrm{C}}=\sqrt{2} \mathrm{R}\)

b

\(\mathrm{X}\) is an inductor and \(\mathrm{X}_{\mathrm{L}}=\mathrm{R}\)

c

\(\mathrm{X}\) is an inductor and \(\mathrm{X}_{\mathrm{L}}=\sqrt{2} \mathrm{R}\)

d

\(\mathrm{X}\) is a capacitor and \(\mathrm{X}_{\mathrm{C}}=\mathrm{R}\)

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