In the expression Vc(t) = Vo e^{-t/r}, what does r denote?

• A. The Time Constant
• B. The Initial Voltage
• C. The Resistance
• D. The Final Voltage

Answer: (A)

The expression describes exponential decay governed by a time scale. In Vc(t) = Vo e^{-t/r}, the exponent must be dimensionless, so r has units of time and represents the time constant. This time constant, often written as tau, sets how fast the voltage across the capacitor decays: after a time equal to r, Vc drops to Vo/e. In an RC circuit, this time constant equals RC, the product of resistance and capacitance, which controls the rate of the discharge. It is not the initial voltage (that is Vo), not the resistance by itself, and not the final voltage (which tends toward zero in a discharge).