Suppose we have a capacitance C discharging through a resistance R. A. The time constant ττ is the interval required for the voltage to rise to 2 times from its initial value.
B. The time constant ττ is the interval required for the voltage to fall to ln(2) ≅ 0.693ln⁡ times from its initial value. C. The time constant ττ is the interval required for the voltage to fall to exp(−1) ≅ 0.368 times its initial value.
D. The time constant ττ is the interval required for the voltage to rise to exp(−1) ≅ 0.368 times its initial value.
In physics, the half-life is often used to characterize exponential decay of physical quantities such as radioactive substances. The half-life is the time required for the quantity to decay to half of its initial value. The time constant for the voltage on a capacitance discharging through a resistance is τ = RC. Find an expression for the half-life of the voltage in terms of R and C.