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

JEE Advanced · 2011 · 10 Apr 2011 · Paper 2 · Alternating Current

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

1.25

, the time constant (in millisecond) of the circuit is

Answer: 4

Solution

Impedance:

Z = R^{2} + \frac{1}{( ω C ) ^{2}} = R 1.25

. Squaring:

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

, giving

\frac{1}{( ω C ) ^{2}} = 0.25 R^{2}

. Therefore

ω C = \frac{2}{R}

, so

R C = \frac{2}{ω} = \frac{2}{500} = 4

ms.

JEE Advanced · 2011 · 10 Apr 2011 · Paper 2 · Integer answer

Practise more: all JEE Advanced PYQs on Alternating Current →

More JEE Advanced questions on Alternating Current

Consider a circuit consisting of a capacitor of capacitance $C$ and a coil with $N$ turns per unit length, cross sectional area $S$ and length $d$ , where $d^{2} ≫ S$ . There is another coil of length $d /2$ , cross sectional area $S /2$ and $2 N$ turns per unit length completel …
JEE Advanced 2026View solution →
A circuit with an electrical load having impedance $Z$ is connected with an AC source as shown in the diagram. The source voltage varies in time as $V (t) = 300 sin (400 t) V$ , where $t$ is time in s. List-I shows various options for the load. The possible currents …
JEE Advanced 2025View solution →
A series LCR circuit is connected to a $45 sin (ω t)$ Volt source. The resonant angular frequency of the circuit is $1 0^{5} rad s^{- 1}$ and current amplitude at resonance is $I_{0}$ . When the angular frequency of the source is …
JEE Advanced 2023View solution →
In a circuit, a metal filament lamp is connected in series with a capacitor of capacitance $C μ F$ across a 200 V, 50 Hz supply. The power consumed by the lamp is 500 W while the voltage drop across it is 100 V. Assume that there is no inductive load in the circuit. …
JEE Advanced 2021View solution →
In a circuit, a metal filament lamp is connected in series with a capacitor of capacitance $C μ F$ across a 200 V, 50 Hz supply. The power consumed by the lamp is 500 W while the voltage drop across it is 100 V. Assume that there is no inductive load in the circuit. …
JEE Advanced 2021View solution →
In the circuit shown, $L = 1 μ H, C = 1 μ F$ and $R = 1 k Ω$ . They are connected in series with an a.c. source $V = V_{0} sin ω t$ as shown. Which of the following options is/are correct?
JEE Advanced 2017View solution →