A series R-C combination is connected to an AC voltage of angular frequency If the impedance of the R-C circuit is the time constant (in millisecond) of the circuit is [2011]

Question

A series R-C combination is connected to an AC voltage of angular frequency $ω = 500 rad/s .$ If the impedance of the R-C circuit is $R \sqrt{1.25},$ the time constant (in millisecond) of the circuit is [2011]

Smart Achievers · Accepted Answer

(4)

$Time constant, T = R C$

$Impedance Z = \sqrt{R^{2} + {(\frac{1}{ω C})}^{2}}$

$Given Z = R \sqrt{1.25}$

$∴$ $R \sqrt{1.25} = \sqrt{R^{2} + {(\frac{1}{ω C})}^{2}}$

$∴$ $R C = \frac{2}{ω} = \frac{2}{500} \times 1000 ms$

$∴$ $R C = 4 ms$

Solution

Q.
A series R-C combination is connected to an AC voltage of angular frequency $ω = 500 rad/s .$ If the impedance of the R-C circuit is $R \sqrt{1.25},$ the time constant (in millisecond) of the circuit is [2011]

Ans.
(4)

$Time constant, T = R C$

$Impedance Z = \sqrt{R^{2} + {(\frac{1}{ω C})}^{2}}$

$Given Z = R \sqrt{1.25}$

$∴$ $R \sqrt{1.25} = \sqrt{R^{2} + {(\frac{1}{ω C})}^{2}}$

$∴$ $R C = \frac{2}{ω} = \frac{2}{500} \times 1000 ms$

$∴$ $R C = 4 ms$

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Solution

Q. A series R-C combination is connected to an AC voltage of angular frequency ω=500 rad/s. If the impedance of the R-C circuit is R1.25, the time constant (in millisecond) of the circuit is [2011]

Ans. (4) Time constant, T=RC Impedance Z=R2+(1ωC)2 Given Z=R1.25 ∴ R1.25=R2+(1ωC)2 ∴ RC=2ω=2500×1000 ms ∴ RC=4 ms

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Q.
A series R-C combination is connected to an AC voltage of angular frequency $ω = 500 rad/s .$ If the impedance of the R-C circuit is $R \sqrt{1.25},$ the time constant (in millisecond) of the circuit is [2011]

Ans.
(4)

$Time constant, T = R C$

$Impedance Z = \sqrt{R^{2} + {(\frac{1}{ω C})}^{2}}$

$Given Z = R \sqrt{1.25}$

$∴$ $R \sqrt{1.25} = \sqrt{R^{2} + {(\frac{1}{ω C})}^{2}}$

$∴$ $R C = \frac{2}{ω} = \frac{2}{500} \times 1000 ms$

$∴$ $R C = 4 ms$