Question

A capacitor with initial voltage of 12 V is discharging through a resistor of 1 megaohm. The Voltages at different times are below

t(s) 0 2 4 6 8 10 12

V(v) 12 8 5.5 3.5 2.5 1.5 1.0

Find time constant of RC circuit and find capacitance

Answer 1

Given

capacitor initial voltage is V0 = 12 V , discharging through a resistor of resistance

   R = 1*10^6 ohm
capacitance of the capacitot is C = ?

Voltages at different times are

t(s) 0 2 4 6 8 10 12

V(v) 12 8 5.5 3.5 2.5 1.5 1.0

we know that the capacitor while discharging the voltage at any instant of time is

V(t) = V0*e^(-t/T)
where T is the time constant of RC circuit

   T = R*C

V(t) = V0*e^(-t/R*C)

substituting the values fot t = 2 s, V(t) = 8 V

8 = 12*e^(-2/T)

T = 4.933 s

and T = R*C ==> C = T/R = 4.933/(1*10^6) F = 4.933*10^-6 F = 4.933 micro farad