Question
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?
Answer Options
- A) Point 1
- B) Point 3
- C) Point 7
- D) Point 8
Correct Answer: A
Explanation
To determine the impedance, we first calculate the capacitive reactance (X_C) and then express the impedance in rectangular form (Z = R - jX_C). The capacitance is C = 19 \times 10^{-12} \text{ F} and the frequency is f = 21.2 \times 10^6 \text{ Hz}. X_C = \frac{1}{2\pi f C} = \frac{1}{2\pi (21.2 \times 10^6)(19 \times 10^{-12})} \approx 396.5 \Omega The impedance is Z = 300 - j396.5 \Omega. This point must be plotted where R = 300 on the positive X-axis and X is approximately -400 on the negative Y-axis.
Consulting Figure E5-1, the horizontal axis scale is resistive (R), and the vertical axis scale is reactive (X). Point 1 is located at approximately R=+300 and X \approx -400. Therefore, Point 1 best represents the impedance of this capacitive circuit.
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