Question

What is the unit for time constant?

Answer 1

The unit for the time constant is seconds (s).

In an electrical circuit, the time constant (\( \tau \)) is typically used in contexts involving resistors and capacitors (RC circuits) or resistors and inductors (RL circuits). It represents the time it takes for the voltage across a capacitor (or the current through an inductor) to either rise or fall to approximately 63% of its final value in response to a change in the circuit.

1. For an RC circuit:  
   

  \( \tau = R \times C \)  
  where \( R \) is resistance in ohms (Ω), and \( C \) is capacitance in farads (F).

1. For an RL circuit:  
   

  \( \tau = \frac{L}{R} \)  
  where \( L \) is inductance in henries (H), and \( R \) is resistance in ohms (Ω).

So, in both cases, the time constant has units of seconds because:

1. For RC circuits, \( \text{Ω} \times \text{F} = \text{s} \).
   

1. For RL circuits, \( \frac{\text{H}}{\text{Ω}} = \text{s} \).