*Question E7C04:
How does an impedance-matching circuit transform a complex impedance to a resistive impedance?*  

*Correct Answer is  C: It cancels the reactive part of the impedance and changes the resistive part to the desired value*  

### AI Response: (may contain errors)  

Impedance matching is a crucial concept in radio and electronics, ensuring maximum power transfer between components by transforming a complex impedance into a purely resistive one.

### Correct Answer: C
**Explanation:**

1. **Cancelling Reactive Part:**
   - A complex impedance consists of a resistive part (real) and a reactive part (imaginary).
   - The reactive part can be inductive (positive reactance) or capacitive (negative reactance).
   - An impedance-matching circuit uses components like inductors and capacitors to cancel out this reactive part, making the impedance purely resistive.

2. **Changing Resistive Part:**
   - Once the reactive part is cancelled, the circuit can adjust the resistive part to match the desired value.
   - This is often done using transformers or specific network configurations (e.g., L-networks, T-networks).

### Why Other Choices Are Incorrect:

- **Choice A:**
  - Introducing negative resistance is not a method used in impedance matching. Negative resistance is a concept used in oscillators and amplifiers, not for cancelling impedance.

- **Choice B:**
  - Transconductance is a property of certain electronic components (like transistors) and is not used to cancel reactive impedance.

- **Choice D:**
  - Reactive currents are not dissipated in resistances. Instead, they are managed by reactive components (inductors and capacitors) to achieve impedance matching.

### Useful Formula:

The impedance $Z$ can be expressed as:
$$ Z = R + jX $$
where:
- $R$ is the resistive part.
- $X$ is the reactive part (inductive or capacitive).

The goal of impedance matching is to adjust $X$ to zero and set $R$ to the desired value for maximum power transfer.