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.
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