*Question E5C10:
Which point on Figure E5-1 best represents the impedance of a series circuit consisting of a 400-ohm resistor and a 38-picofarad capacitor at 14 MHz?*  

*Correct Answer is  B: Point 4*  

### AI Response: (may contain errors)  

To determine the impedance of a series circuit consisting of a resistor and a capacitor, we need to calculate the total impedance, which is a complex number consisting of a real part (resistance) and an imaginary part (reactance).

### Step-by-step Explanation:

1. **Resistance ($R$):**  
   The resistance is given as 400 ohms.

2. **Capacitive Reactance ($X_C$):**  
   The capacitive reactance can be calculated using the formula:  
   $$X_C = \frac{1}{2 \pi f C}$$  
   where:
   - $f = 14 \, \text{MHz} = 14 \times 10^6 \, \text{Hz}$
   - $C = 38 \, \text{pF} = 38 \times 10^{-12} \, \text{F}$

   Plugging in the values:  
   $$X_C = \frac{1}{2 \pi \times 14 \times 10^6 \times 38 \times 10^{-12}}$$  
   $$X_C \approx 300 \, \text{ohms}$$

3. **Total Impedance ($Z$):**  
   The total impedance of the series circuit is:  
   $$Z = R - jX_C = 400 - j300 \, \text{ohms}$$  
   This is because capacitive reactance is negative in the imaginary component.

### Interpretation on the Impedance Plane:

- **Real Part (Resistance):** 400 ohms
- **Imaginary Part (Reactance):** -300 ohms (capacitive)

On the impedance plane (Figure E5-1), this point would be located at 400 on the real axis and -300 on the imaginary axis.

### Why Point 4 is Correct:

- **Point 4** represents an impedance with a positive real part (resistance) and a negative imaginary part (capacitive reactance), matching $400 - j300$ ohms.

### Why Other Choices are Incorrect:

- **Point 2:** Likely represents an impedance with a positive real part and a positive imaginary part (inductive reactance), which does not match our calculation.
- **Point 5:** Could represent a different combination of resistance and reactance, not matching $400 - j300$ ohms.
- **Point 6:** Likely represents an impedance with a negative real part or a different reactance, which does not match our calculation.

By understanding these calculations and interpretations, you can correctly identify the impedance on the impedance plane.