A series $R-C$ combination is connected to an $\mathrm{AC}$ voltage of angular frequency $\omega=500…
A series $R-C$ combination is connected to an $\mathrm{AC}$ voltage of angular frequency $\omega=500 \mathrm{rad} / \mathrm{s}$. If the impedance of the $R-C$ circuit is $R \sqrt{1.25}$, the time constant (in millisecond) of the circuit is
Solution
$Z=\sqrt{R^2+X_C^2}=R \sqrt{1.25}$
$
\therefore \quad R^2+X_C^2=1.25 R^2
$
or $\quad X_C=\frac{R}{2}$
or $\quad \frac{1}{\omega C}=\frac{R}{2}$
$\begin{aligned} \therefore \text { Time constant } & =C R=\frac{2}{\omega} \\ & =\frac{2}{500} \mathrm{~s}=4 \mathrm{~ms}\end{aligned}$
$\therefore$ Answer is 4 .
Analysis of Question
(i) Question is very simple.
(ii) I think this is one of the simplest formula based question of this paper.
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