What is the meaning of the term “time constant of an RC circuit”? The time required to charge the capacitor in the circuit to:
• RC time constant (τ) in a resistor–capacitor circuit • Exponential charging formula: V(t) = Vsup · (1 − e^{−t/RC}) • Special case when t = τ = RC and how much the capacitor has charged as a percentage of supply voltage
• Write the charging equation V(t) = Vsup · (1 − e^{−t/RC}) and substitute t = RC (i.e., t = τ). What does the expression simplify to? • Recall that e^{−1} is about 0.37. If the remaining uncharged portion is about 37%, what percentage has been charged? • Which answer choice is closest to 1 − e^{−1}, expressed as a percentage of the supply voltage?
• Be sure you are thinking about charging, not discharging, when you interpret the formula • Confirm that τ = R × C has units of seconds, and that at t = τ the exponent becomes −1 • Double-check which answer choice matches (1 − e^{−1}) × 100%, not e^{−1} × 100%
No comments yet
Be the first to share your thoughts!