*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 400-ohm resistor and a 38-picofarad capacitor at 14 MHz, we need to calculate the capacitive reactance and then find the total impedance.

1. **Calculate the capacitive reactance ($X_C$)**:  
   The formula for capacitive reactance is given by:  
   $$X_C = \frac{1}{2 \pi f C}$$  
   where:
   - $f$ = frequency in hertz (14 MHz = $14 \times 10^6$ Hz)
   - $C$ = capacitance in farads (38 picofarads = $38 \times 10^{-12}$ F)

   Plugging in the values:  
   $$X_C = \frac{1}{2 \pi (14 \times 10^6) (38 \times 10^{-12})}$$  
   $$X_C \approx \frac{1}{3.14 \times 14 \times 10^{-6} \times 38 \times 10^{-12}}$$  
   $$X_C \approx \frac{1}{2.5 \times 10^{-6}} \approx 400 \, \text{ohms}$$  

2. **Total impedance ($Z$)**:  
   In a series circuit, the total impedance is given by:  
   $$Z = R + jX_C$$  
   where:
   - $R$ = resistance (400 ohms)
   - $X_C$ = capacitive reactance (approximately -400 ohms, since it is capacitive)

   Therefore, the total impedance can be expressed as:  
   $$Z = 400 - j400$$  

3. **Magnitude of the impedance**:  
   The magnitude of the impedance can be calculated using:  
   $$|Z| = \sqrt{R^2 + X_C^2}$$  
   $$|Z| = \sqrt{400^2 + (-400)^2} = \sqrt{160000 + 160000} = \sqrt{320000} \approx 565.7 \, \text{ohms}$$  

4. **Phase angle**:  
   The phase angle ($\phi$) can be calculated as:  
   $$\tan(\phi) = \frac{X_C}{R} = \frac{-400}{400} = -1$$  
   Thus, $\phi = -45^\circ$.

### Explanation of the Correct Answer:
- **Point 4** represents the impedance of a series circuit with a resistive and reactive component, which matches our calculated impedance of approximately $400 - j400$ ohms. This indicates a significant reactive component, which is consistent with the presence of a capacitor.

### Why Other Choices Are Incorrect:
- **Point 2**: Likely represents a purely resistive load or a different reactance that does not match our calculated impedance.
- **Point 5**: May indicate a higher impedance or a different phase angle, not aligning with our calculated values.
- **Point 6**: Similar to Point 2, it likely represents a different impedance configuration that does not correspond to the series combination of a 400-ohm resistor and a 38-picofarad capacitor.

### Summary:
- The correct answer is **Point 4** because it accurately reflects the impedance of the given series circuit at 14 MHz, while the other points do not match the calculated impedance characteristics.