RL Circuit Time Constant Quiz with Answers: Test Your Knowledge

📚 Quick Study Guide

• ⚛️ An RL circuit contains a resistor (R) and an inductor (L) connected in series or parallel.
• ⏱️ The time constant ($\tau$) for an RL circuit is a measure of how long it takes for the current in the circuit to reach approximately 63.2% of its final value during charging or to decay to 36.8% of its initial value during discharging.
• 📐 For a series RL circuit, the time constant is given by: $\tau = \frac{L}{R}$, where L is the inductance in Henrys and R is the resistance in Ohms.
• ⚡ In an RL circuit, the voltage across the inductor is given by $V_L(t) = V_0 e^{-\frac{t}{\tau}}$, and the current is given by $I(t) = I_0 (1 - e^{-\frac{t}{\tau}})$ during charging, where $V_0$ and $I_0$ are the initial voltage and current, respectively.
• 💡 After 5 time constants ($5\tau$), the circuit is generally considered to have reached its steady-state condition.

Practice Quiz

1. What is the time constant ($\tau$) of a series RL circuit with an inductance (L) of 2 H and a resistance (R) of 4 Ohms?
   1. A) 0.5 s
   2. B) 2 s
   3. C) 8 s
   4. D) 6 s
2. In an RL circuit, approximately what percentage of the final current is reached after one time constant?
   1. A) 36.8%
   2. B) 63.2%
   3. C) 86.5%
   4. D) 95%
3. What happens to the time constant of an RL circuit if the inductance (L) is doubled and the resistance (R) remains constant?
   1. A) It is halved.
   2. B) It remains the same.
   3. C) It is doubled.
   4. D) It is quadrupled.
4. After how many time constants is an RL circuit generally considered to have reached its steady state?
   1. A) 1
   2. B) 3
   3. C) 5
   4. D) 10
5. If the resistance in a series RL circuit is increased while the inductance remains constant, what happens to the time constant?
   1. A) Increases
   2. B) Decreases
   3. C) Remains the same
   4. D) Fluctuates randomly
6. An RL circuit has a time constant of 0.2 seconds. If the resistance is 10 Ohms, what is the inductance?
   1. A) 0.02 H
   2. B) 2 H
   3. C) 5 H
   4. D) 10 H
7. What is the effect of a larger time constant in an RL circuit on the rate of current increase during charging?
   1. A) Faster current increase
   2. B) Slower current increase
   3. C) No effect on current increase
   4. D) Unpredictable current increase