Instantaneous Values of Capacitor

On occasion it will be necessary to determine the voltage or current at a particular instant of time that is not an integral multiple of $\tau$, as in the previous sections. For example, if the voltage $v_C$ may be required at t = 5 ms, which does not correspond to a particular value of $\tau$. [Fig. 1] reveals that $(1 - e^{-t/\tau})$ is approximately $0.93$ at $t = 5 ms = 2.5\tau$, resulting in $v_C = 20(0.93) =18.6 V$. Additional accuracy can be obtained simply by substituting $t = 5 ms$ into the equation and solving for $v_C$. Thus, The results are close, but accuracy beyond the tenths place is suspect using [Fig. 1]. The above procedure can also be applied to any other equation introduced in this chapter for currents or voltages.

Time to reach a particular voltage or current

There are also occasions when the time to reach a particular voltage or current is required. The procedure is complicated somewhat by the use of natural logs ($log_e$, or $ln$), but today's calculators are equipped to handle the operation with ease. There are two forms that require some development. First, consider the following sequence: but therefore;