*Question E5C12:
Which point on Figure E5-1 best represents the impedance of a series circuit consisting of a 300-ohm resistor and a 19-picofarad capacitor at 21.200 MHz?*  

*Correct Answer is  A: Point 1*  

### AI Response: (may contain errors)  

To determine the impedance of a series circuit consisting of a 300-ohm resistor and a 19-picofarad capacitor at 21.200 MHz, we need to calculate the total impedance, which is a combination of the resistive and reactive components.

### Step-by-step Explanation:

1. **Calculate Capacitive Reactance ($X_C$):**

   The capacitive reactance is given by the formula:  
   $$X_C = \frac{1}{2 \pi f C}$$  
   where:
   - $f = 21.200 \, \text{MHz} = 21.200 \times 10^6 \, \text{Hz}$
   - $C = 19 \, \text{pF} = 19 \times 10^{-12} \, \text{F}$

   Plugging in the values:  
   $$X_C = \frac{1}{2 \pi \times 21.200 \times 10^6 \times 19 \times 10^{-12}} \approx 397 \, \text{ohms}$$

2. **Determine Total Impedance ($Z$):**

   The total impedance of a series circuit is the sum of the resistive and reactive components:  
   $$Z = R + jX_C$$  
   where:
   - $R = 300 \, \text{ohms}$
   - $X_C = -397 \, \text{ohms}$ (capacitive reactance is negative in the imaginary plane)

   Therefore, the impedance is:  
   $$Z = 300 - j397 \, \text{ohms}$$

3. **Locate the Point on the Impedance Plane:**

   On the impedance plane (complex plane), the real part (resistance) is plotted on the horizontal axis, and the imaginary part (reactance) is plotted on the vertical axis. A negative reactance indicates a point below the horizontal axis.

   - **Point 1**: Represents $300 - j397 \, \text{ohms}$, which matches our calculated impedance.

### Why Other Choices are Incorrect:

- **Point 3**: Would represent a different combination of resistance and reactance, not matching $300 - j397 \, \text{ohms}$.
- **Point 7**: Would also represent a different impedance, likely with a different resistive or reactive component.
- **Point 8**: Similarly, this point would not match the calculated impedance of $300 - j397 \, \text{ohms}$.

Thus, **Point 1** is the correct representation of the impedance for the given series circuit at 21.200 MHz.