Question

Is Thevenin's theorem AC or DC?

Answer 1

**Thevenin's Theorem** applies to both **AC (Alternating Current)** and **DC (Direct Current)** circuits. The theorem itself is a fundamental concept in circuit analysis and can be used to simplify a complex electrical network into a simple equivalent circuit, which consists of a single voltage source (Thevenin voltage) in series with a single resistor (Thevenin resistance).

### How it applies to both AC and DC:

1. **In DC Circuits:**
   - Thevenin's Theorem simplifies a network of resistors and independent or dependent DC voltage sources into a single voltage source \( V_{\text{th}} \) in series with a resistance \( R_{\text{th}} \).
   - The equivalent voltage \( V_{\text{th}} \) is found by analyzing the open-circuit voltage at the terminals of interest.
   - The equivalent resistance \( R_{\text{th}} \) is determined by "turning off" the independent sources (setting voltage sources to zero, meaning replacing them with short circuits, and current sources with open circuits) and calculating the resistance between the terminals.

2. **In AC Circuits:**
   - In AC analysis, the same principle holds, but the components of the circuit, like impedance, have to be considered because of the presence of inductors, capacitors, and AC voltage sources.
   - In this case, the Thevenin equivalent consists of an AC voltage source \( V_{\text{th}} \) and an impedance \( Z_{\text{th}} \). Impedance \( Z_{\text{th}} \) replaces the simple resistance \( R_{\text{th}} \) and includes resistive, inductive, and capacitive elements.
   - The equivalent AC voltage \( V_{\text{th}} \) is found using phasor analysis, which considers both magnitude and phase of the voltages and currents in the circuit.

### Key Differences:
- **In DC circuits,** you deal only with resistance (R) and voltage sources.
- **In AC circuits,** impedance (Z) replaces resistance, and both the magnitude and phase angle of the voltages and currents are considered.

So, **Thevenin's Theorem is applicable to both AC and DC circuits**, but the method of analysis varies slightly due to the nature of AC involving impedance, while DC involves simple resistance.

Answer 2

Thevenin's Theorem applies to both AC and DC circuits.

- In **DC circuits**, it simplifies a complex network of resistances and voltage sources to a single voltage source (Thevenin equivalent voltage) in series with a single resistance (Thevenin equivalent resistance).
  
- In **AC circuits**, it can also be used, but instead of just resistance, it simplifies the circuit using impedance (which accounts for resistances, inductances, and capacitances) along with a Thevenin equivalent voltage.

So, Thevenin's Theorem is applicable to both types of circuits.