*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 a frequency of 21.200 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 (21.200 MHz = $21.200 \times 10^6$ Hz)
   - $C$ = capacitance in farads (19 picofarads = $19 \times 10^{-12}$ F)

   Plugging in the values:  
   $$X_C = \frac{1}{2 \pi (21.200 \times 10^6) (19 \times 10^{-12})}$$  
   $$X_C \approx \frac{1}{2 \pi (21.200 \times 10^6) (19 \times 10^{-12})} \approx 0.0004 \, \text{ohms}$$  
   (This is a rough estimate; you can calculate it for more precision.)

2. **Total impedance ($Z$)**:  
   In a series circuit, the total impedance is given by:  
   $$Z = R + jX_C$$  
   where:
   - $R$ = resistance (300 ohms)
   - $X_C$ = capacitive reactance (which is negative in the context of impedance)

   Therefore, the impedance can be expressed as:  
   $$Z = 300 - jX_C$$  

3. **Why the correct answer is Point 1**:  
   - Point 1 on Figure E5-1 represents a point in the complex plane where the real part (resistance) is 300 ohms and the imaginary part (reactance) is negative, indicating a capacitive circuit. Since the capacitive reactance is small compared to the resistance, the impedance will be close to 300 ohms.

4. **Why the other choices are incorrect**:  
   - **Point 3**: This point likely represents a higher reactance or a different impedance configuration, not matching our calculated values.
   - **Point 7**: This point may indicate a purely resistive or inductive circuit, which does not apply to our series circuit with a capacitor.
   - **Point 8**: Similar to Point 7, this point does not reflect the correct impedance characteristics of a series resistor-capacitor circuit.

In summary, the correct answer is Point 1 because it accurately represents the impedance of a 300-ohm resistor in series with a small capacitive reactance at the specified frequency.