91Ó°ÊÓ

In the R-C circuit, a resistor and capacitor are connected to an energy source in the electrical circuit.

The current flowing in the circuit can be written as:

$l=l_0{e}^{-t/RC}$

Here R is the resistance of the resister, and C is the capacitance of the capacitor. RC is the time constant for the capacitor.

The equation for electric current in an R-C circuit is:

$$\begin{gathered} l=l_0{e}^{-t/RC} \\ \frac{l}{l_0}=e^{-t/RC} \\ \frac{-t}{RC}=\ln \frac{l}{l_0} \\ R=\frac{-t}{\ln \left(\frac{l}{l_0}\right)×C} \end{gathered}$$

In the above equation, if the initial current $l_0$is known and the discharge current can be calculated and C is known. So, during the discharging process, the time of discharge can be determined. Now, all the variables are known in the equation, so then R can be measured.

Thus, the large resistance would be measured by knowing the initial and discharging current for a known capacitance in a specific time constant.