The charging time constant of a circuit consisting of a capacitor is the time taken for the charge i

Question

The charging time constant of a circuit consisting of a capacitor is the time taken for the charge in the capacitor to become __________ % of the initial charge.

Examoogle · Accepted Answer

63

Explanation: The charging time constant ($	au$) of an RC circuit is defined as the time taken for the capacitor to charge to approximately 63.2% of its maximum steady-state voltage or charge. This is derived from the exponential charging equation $q(t) = Q_{max}(1 - e^{-t/	au})$.

Working Principle: When a capacitor charges through a resistor, the voltage builds up exponentially. At $t = 	au = RC$, the term $(1 - e^{-t/	au})$ becomes $(1 - e^{-1})$, which is approximately $1 - 0.368 = 0.632$. Thus, the capacitor has reached 63.2% of the applied source potential.

Key Formulas: $q(t) = Q_0(1 - e^{-\frac{t}{RC}})$ — Instantaneous charge during charging; $	au = RC$ — Time constant of the RC circuit

Key Points: One time constant is defined as $t = RC$.; After $5	au$ (5 time constants), the capacitor is considered fully charged (approx 99.3%).; The discharge time constant is the time taken to reach 36.8% (or 1 - 0.632) of the initial charge.

Advantages: Predictable circuit behavior; Simple relationship between R, C, and time

Disadvantages: Does not reach 100% theoretically in finite time; Depends on component tolerance (R and C variations)

Applications: Timing circuits (timers); Pulse shaping networks; Smoothing filters

Additional Info: The value 63.2% arises from the natural logarithm base $e \approx 2.718$.. Option C (37%) is the value to which the capacitor drops during the discharge phase after one time constant.

Answer: B is correct — The charging time constant represents the time taken for a capacitor to charge to approximately 63.2% of its maximum value.

Exam Tip: Always remember that in RC charging, it reaches ~63% of the final value, whereas in discharge, it drops by ~63% of its initial value (retaining ~37%).

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