Solved Examples: Calculating Time Constant in RC Circuits

📚 Quick Study Guide

• ⚡️ An RC circuit contains a resistor (R) and a capacitor (C).
• ⏱️ The time constant ($\tau$) represents the time it takes for the capacitor to charge to approximately 63.2% of its maximum voltage (or discharge to 36.8% of its initial voltage).
• 📐 The formula for the time constant is: $\tau = RC$, where R is the resistance in ohms and C is the capacitance in farads.
• 💡 A larger time constant means a slower charging/discharging process, while a smaller time constant means a faster process.
• 📊 After 5 time constants (5$\tau$), the capacitor is considered to be virtually fully charged or discharged.

🧪 Practice Quiz

1. What is the time constant of an RC circuit with a resistance of 10 kΩ and a capacitance of 100 μF?
   1. 0.1 s
   2. 1 s
   3. 10 s
   4. 100 s
2. If an RC circuit has a time constant of 2 seconds and a resistance of 4 kΩ, what is the capacitance?
   1. 0.5 mF
   2. 5 mF
   3. 50 mF
   4. 500 mF
3. An RC circuit has a 1 MΩ resistor and a 1 μF capacitor. How long will it take for the capacitor to approximately fully charge?
   1. 1 s
   2. 2 s
   3. 3 s
   4. 5 s
4. What happens to the time constant if you double both the resistance and capacitance in an RC circuit?
   1. It remains the same.
   2. It doubles.
   3. It quadruples.
   4. It halves.
5. In an RC discharging circuit, after one time constant, approximately what percentage of the initial voltage remains across the capacitor?
   1. 36.8%
   2. 63.2%
   3. 0%
   4. 100%
6. If the resistance in an RC circuit is decreased while the capacitance remains constant, what happens to the time constant?
   1. It increases.
   2. It decreases.
   3. It remains the same.
   4. It oscillates.
7. An RC circuit has a time constant of 0.5 seconds. If the capacitor is initially uncharged and the voltage source is applied, how long will it take for the capacitor voltage to reach approximately 63.2% of the source voltage?
   1. 0.25 s
   2. 0.5 s
   3. 1 s
   4. 2.5 s