The time constant for the network shown below will be :
\(\dfrac{2}{3}\) sec
To find the time constant of the given network, we analyze the circuit shown in the image. The circuit consists of a 1 H inductor and resistors.
The time constant \( \tau \) of an RL circuit is given by the formula:
\(\tau = \dfrac{L}{R_{\text{eq}}}\)
where \( L \) is the inductance and \( R_{\text{eq}} \) is the equivalent resistance seen by the inductor.
Step-by-step calculation:
Determine the equivalent resistance \( R_{\text{eq}} \) across the inductor:
- The 1 Ω resistor in series with the inductor is in parallel with the series combination of 1 Ω and 1 Ω resistors.
- Calculate the series resistance: \(R_{\text{series}} = 1 + 1 = 2 \, \Omega\).
- Calculate the equivalent resistance: \(R_{\text{eq}} = \left(\dfrac{1}{1} + \dfrac{1}{2}\right)^{-1} = \left(\dfrac{2+1}{2}\right)^{-1} = \dfrac{2}{3} \, \Omega\)
Substitute the values into the time constant formula:
- \(\tau = \dfrac{1 \, \text{H}}{\dfrac{2}{3} \, \Omega} = \dfrac{3}{2}\) seconds.
After reviewing, the given options do not match this calculation. The calculation has verified the original given answer is incorrect.
To get the correct time constant, adjustments or context in the question or revisiting any assumptions may be needed.
Similar Questions
For series RLC circuit given below in figure, choose the correct answer based on Kirchoff's voltage law from following:
The RLC circuit given in figure below can be solved
A. Current i(t) can be solved using KVL
B. Current i(t) can be solved using KCL
C. Current i(t) can be solved using fourier transform
D. Current i(t) can be solved using laplace transform
E. Current i(t) can be solved using Fourier series
Choose the correct answer from the options given below:
Match the following in the context of RLC series circuit :
List - I List - II (a) Under damped (i) \(\xi=1\) (b) Critically damped (ii) \(\xi \gt 1\) (c) Quality factor (iii) \(\dfrac{1}{2\xi}\) (d) Over damped (iv) \(\xi \lt 1\) Codes :
Which of the following circuits will have transients ?
1. Resistive
2. R-L
3. R-C
4. R-L-CWhich is correct ?
Important Questions from Transient Analysis
Consider the following statements regarding circuit elements:
1. The voltage across a capacitor cannot change instantaneously.
2. The current through an inductor cannot change instantaneously.
3. The current through a capacitor is always a continuous function.
4. The voltage across an inductor is always a continuous function.
Which of these statements are correct?
At t = 0+ an inductor with zero initial condition acts as a/an
During discharging of a capacitor of C = 100 µF through a resistance of 1 KΩ applied with 50 V, the voltage at the time of the it's time constant is
Name that transient which is produced when a circuit, which is originally dead, is energized.
What is the value of current at t = 5T instant in an RC network fed with voltage V where T is time constant?
