FCC Exam Question: 3-15B4

What is the time constant of a circuit having a 220-microfarad capacitor and a 1-megohm resistor in parallel?

A. 220 seconds.
B. 22 seconds.
C. 2.2 seconds.
D. 0.22 seconds.
Correct Answer: A

Explanation: The time constant (τ) of a resistor-capacitor (RC) circuit, such as one with a resistor and capacitor in parallel or series, is a fundamental concept in radio theory. It represents the time required for the capacitor to charge to approximately 63.2% of the applied voltage or discharge to 36.8% of its initial voltage. The formula for the time constant is τ = R * C, where R is resistance in ohms and C is capacitance in farads. Given: * Resistance (R) = 1 megohm (1 MΩ) = 1,000,000 ohms * Capacitance (C) = 220 microfarads (220 µF) = 0.000220 farads Plugging these values into the formula: τ = 1,000,000 Ω * 0.000220 F τ = 220 seconds Thus, the time constant is 220 seconds. Options B, C, and D are incorrect because they result from miscalculations or incorrect unit conversions, such as forgetting to convert megohms to ohms or microfarads to farads.

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Includes Elements 1, 3, 6, 7R, 8, and 9.