Type 2 (Combination of Resistance and Capacitor)  Transient Analysis Time Domain Analysis  EXTC  Summary and Q&A
TL;DR
Type 2 transient response in electrical circuits involves a combination of resistance and capacitance or resistance and inductance.
Key Insights
 🅰️ Type 2 transient response involves a combination of resistance and either capacitance or inductance.
 😚 In the first case, when the switch is open, the circuit has no closed path, resulting in zero current.
 😚 In the second case, when the switch is closed, the uncharged capacitor causes a short circuit, allowing current to flow.
 💼 The current in the second case is determined using Kirchhoff's Voltage Law.
 🔠 In the third case, for t > 0, the circuit remains the same, and the voltage across the capacitor is determined using the formula 1/C * ∫(i(t) dt).
 ☠️ The rate of change of current over time is found by differentiating the equation derived from Kirchhoff's Voltage Law.
Questions & Answers
Q: What is the difference between Type 2 transient response involving a combination of resistance and capacitance and resistance and inductance?
The main difference is that in the case of capacitance, the capacitor is uncharged and needs to accept current to become charged, so the circuit must be closed. In the case of inductance, the inductor opposes the current initially and requires the circuit to be open.
Q: How is the current determined in the second case of Type 2 transient response?
The current in the second case is determined using Kirchhoff's Voltage Law. The equation is 1000 * i(0+) = 100, where i(0+) represents the current at t = 0+ (immediately after the switch is closed). Solving for i(0+), we find it to be 0.1 Amperes.
Q: How is the voltage across the capacitor determined in the third case of Type 2 transient response?
The voltage across the capacitor is determined using the formula 1/C * ∫(i(t) dt), where C is the capacitance of the capacitor. By applying Kirchhoff's Voltage Law, the equation 1000 * i(0+) + 1/(1 * 10^6) * ∫(i(t) dt) = 0 is obtained. The rate of change of current over time is then found by differentiating this equation.
Q: What is the value of the d^2i/dt^2 in the third case of Type 2 transient response?
By differentiating the equation 1000 * d^2i/dt^2 + 1/(1 * 10^6) * di(0+)/dt = 0, we find that d^2i/dt^2 is equal to 10^5 Ampere/second^2.
Summary & Key Takeaways

In the first case, when the switch is open, the circuit consists of a 100V source in series with a 1000 ohm resistance and a 1 microfarad capacitor. The current in this case is zero.

In the second case, when the switch is closed, the uncharged capacitor causes the circuit to become a short circuit, allowing the current to flow. The current is determined using Kirchhoff's Voltage Law and is found to be 0.1 Amperes.

In the third case, for t > 0, the circuit remains the same, and the voltage across the capacitor is determined using the formula 1/C * ∫(i(t) dt). By applying Kirchhoff's Voltage Law, the equation for the current is differentiated to find the rate of change of current over time.