A series R-C combination is connected to an AC voltage of angular frequency = 500 radian/s. If the impedance of the R-C circuit is , the time constant (in millisecond) of the circuit is :

Engineering

Physics

AC Circuit Analysis

Question

A series R-C combination is connected to an AC voltage of angular frequency $ω$ = 500 radian/s. If the impedance of the R-C circuit is $R \sqrt{1 .25}$ , the time constant (in millisecond) of the circuit is :

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$z = R \sqrt{1 .25}$

$\begin{array}{l} τ = RC \\ R^{2} + {(\frac{1}{500 C})}^{2} = Z^{2} \end{array}$

$R^{2} + {(\frac{1}{500 C})}^{2} = R^{2} \times 1 .25$

${(\frac{1}{500 C})}^{2} = 0 .25 R^{2} \Rightarrow \frac{1}{500 C} = 0 .5 R$

$\frac{1}{2500} = RC$

$\frac{1}{250} = RC$

0.004 sec = RC

RC = 4 mill second.