FCC Exam Question: 3-14B2

What is the meaning of the term “time constant of an RC circuit”? The time required to charge the capacitor in the circuit to:

A. 23.7% of the supply voltage.
B. 36.8% of the supply voltage.
C. 57.3% of the supply voltage.
D. 63.2% of the supply voltage.
Correct Answer: D

Explanation: The time constant ($\tau$) of an RC (resistor-capacitor) circuit is a crucial parameter indicating how quickly a capacitor charges or discharges through a resistor. It is calculated by multiplying the resistance (R) in ohms by the capacitance (C) in farads, resulting in a time in seconds. When a capacitor in an RC circuit is charging from a DC supply, one time constant represents the time it takes for the voltage across the capacitor to reach approximately 63.2% of the final applied supply voltage. This value is derived from the exponential charging curve, specifically (1 - 1/e), where 'e' is Euler's number. Conversely, when discharging, it takes one time constant for the capacitor's voltage to fall to 36.8% of its initial voltage. Therefore, option D correctly describes the charging scenario. RC circuits are fundamental in amateur radio for filtering, timing circuits, and waveform shaping.

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