Electromagnetic Induction and Alternating Current 6 Question 13
13. A series $R-C$ combination is connected to an $A C$ voltage of angular frequency $\omega=500 rad / s$. If the impedance of the $R-C$ circuit is $R \sqrt{1.25}$, the time constant (in millisecond) of the circuit is
(2011)
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Answer:
Correct Answer: 13. 4
Solution:
- $Z=\sqrt{R^{2}+X _C^{2}}=R \sqrt{1.25}$
$\therefore R^{2}+X _C^{2}=1.25 R^{2}$ or $X _C=\frac{R}{2}$ or $\frac{1}{\omega C}=\frac{R}{2}$
$\therefore$ Time constant $=C R=\frac{2}{\omega}=\frac{2}{500} s=4 ms$
