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% Final Voltage/Current Values Versus Time Constants

 

 

 
 

         

 

Table 1.  Time Constant Formulas

Description

Formula

Remarks

RC Circuit Time Constant (τ)

τ  = RC

R = resistance (ohms); C = capacitance (F)

RL Circuit Time Constant (τ)

τ  = L / R

R = resistance (ohms); L = inductance (H)

Circuit Charging, voltage v(t), Vi>0

v(t) = Vf - ( Vf - Vi )e-t/τ

initially charged to Vi; Vf = final voltage

Circuit Charging, current i(t), Ii>0

i(t) = If - ( If - Ii )e-t/τ

initially charged with Ii; If = final current

Circuit Charging, voltage v(t), Vi=0

v(t) = Vf ( 1 - e-t/τ )

initially discharged; Vf = final voltage

Circuit Charging, current i(t), Vi=0

i(t) = If ( 1 - e-t/τ )

initially discharged; If = final current

Circuit Discharging, voltage v(t)

v(t) = Vi ( e-t/τ )

Vi = initial voltage; Vf = final voltage

Circuit Discharging, current i(t)

i(t) = Ii ( e-t/τ )

Ii = initial current; If = final current

 

Table 2.  % Final Voltage/Current Values Versus Time Constants

Time Constant τ

Circuit Charging

(initially discharged)

Circuit Discharging

0.1

9.5%

90.5%

0.2

18.1%

81.9%

0.3

25.9%

74.1%

0.4

33%

67%

0.5

39.3%

60.7%

1.0

63.2%

36.8%

2.0

86.5%

13.5%

3.0

95%

5%

4.0

98.2%

1.8%

5.0

99.3%

0.7%