A) 5
B) 4
C) 6
D) 8
Correct Answer: B
Solution :
Time constant = RC Impedance \[=\sqrt{{{R}^{2}}+{{\left( \frac{1}{\omega C} \right)}^{2}}}\] Given impedance \[=R\sqrt{1.25}\] \[\therefore \,R\sqrt{1.25}=\sqrt{{{R}^{2}}+{{\left( \frac{1}{\omega C} \right)}^{2}}}\] \[\therefore \,{{R}^{2}}\sqrt{1.25}={{R}^{2}}+{{\left( \frac{1}{\omega C} \right)}^{2}}\] \[\therefore \,\,\frac{{{R}^{2}}}{4}={{\left( \frac{1}{\omega C} \right)}^{2}}\] \[\therefore \,\,\frac{R}{2}=\frac{1}{\omega C}\] \[\therefore \,\,RC=\frac{2}{\omega }=\frac{2}{500}\times 1000\,ms\] \[\therefore \,\,RC=4\,ms\]
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