Question 508: AC fundamentals

Question

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

Accepted Answer

We have impedance in the circuit
$$Z = \sqrt {{R^2} + {{\left( {{1 \over {\omega C}}} ight)}^2}} $$
However, $$Z = R\sqrt {1.25} $$ and $$R\sqrt {1.25}  = \sqrt {{R^2} + {{\left( {{1 \over {\omega C}}} ight)}^2}}  $$
$$\Rightarrow 0.25{R^2} = {1 \over {{{(\omega C)}^2}}}$$
The time constant is
$$RC = \sqrt {{1 \over {0.25 	imes {{500}^2}}}}  = 4$$ ms

AC fundamentals

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

Integer / Numeric Answer Type