SATHEE: Electromagnetic Induction and Alternating Current 6 Question 13

Electromagnetic Induction and Alternating Current 6 Question 13

13. A series $R - C$ combination is connected to an $A C$ voltage of angular frequency $ω = 500 r a d / s$ . 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:

$Z = \sqrt{R^{2} + X_{C}^{2}} = R \sqrt{1.25}$

$∴ R^{2} + X_{C}^{2} = 1.25 R^{2}$ or $X_{C} = \frac{R}{2}$ or $\frac{1}{ω C} = \frac{R}{2}$

$∴$ Time constant $= C R = \frac{2}{ω} = \frac{2}{500} s = 4 m s$

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Electromagnetic Induction and Alternating Current 6 Question 13

13. A series R−C combination is connected to an AC voltage of angular frequency ω=500rad/s. If the impedance of the R−C circuit is R1.25, the time constant (in millisecond) of the circuit is

Answer:

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13. A series $R - C$ combination is connected to an $A C$ voltage of angular frequency $ω = 500 r a d / s$ . If the impedance of the $R - C$ circuit is $R \sqrt{1.25}$ , the time constant (in millisecond) of the circuit is