Question

Compare three calculated time constant and describe how the difference in the value of the resistance affected the rate of discharge of the capacitor.

RC Circuit	Trendline Equation	Time Constant
RC Circuit with 10 Ω	V(t) = 3.8749e-0.06t	0.9947
RC Circuit with 50 Ω	V(t) = 4.3616e-0.014t	0.9975
RC Circuit with 100 Ω	V(t) = 4.1298e-0.007t	0.998

Answer 1

RC circuit with

resistance R1 = 10 ohm , having the time constant in discharging of a capacitor

T1 = 0.9947

we know that the time constant T = R*C

and T2 = 0.9975 with resistance R2 = 50 ohm

T3 = 0.998 with resistance R2 = 100 ohm

the potential is given by v(t) = V0*e^(-t/T)

T is time constant includes the resistance as the resistance is lage in the circuit so the time constant

we know that the time constant is the time taken for the charge /potential to drop its initial value (1/e)times  

it happens if t = T

v(T) = V0*e^(-T/T) = V0*e^-1 = V0/e = 0.37*V0

v(T) = 0.37*V0