Question

Calculate time constants for each of the RC circuits described in Problem 2-14.

Short answer

The time constants are 0.25s, 0.025s, and 0.000025s respectively

Step-by-step solution

Given information:

$Thecapacitorof0.025\mu Fandresis\tan cesof10M\Omega ,1M\Omega ,and1K\Omega .$

Calculations:

The time constant of the resistor-capacitor circuit is given by:

$$\begin{gathered} \tau =RC \\ \left(i\right)R=10M\Omega andC=0.025\mu F \\ \tau =(10\times {10}^6)\times (0.025\times {10}^{-6})s \\ \tau =0.25s \\ \left(ii\right)R=1M\Omega andC=0.025\mu F \\ \tau =(1\times {10}^6)\times (0.025\times {10}^{-6})s \\ \tau =0.025s \\ \left(iii\right)R=1k\Omega andC=0.025\mu F \\ \tau =(1\times {10}^3)\times (0.025\times {10}^{-6})s \\ \tau =0.000025s \end{gathered}$$