Passive RC Circuit Natural response & Inductor Voltage-Current Relations

     In this lab time constant of a capacitor is determined. R2 = 2.2 KΩ is parallel with C = 22 μF and

R1 = 1 KΩ is series with this two elements. Also, a 5V square voltage with a 1 KHz frequency is

connected to the circuit.

Figure 1: Calculation of Time Constant 

Figure 2: Calculation of a Real Time Constant

Figure 3: A Discharge Graph of a Capacitor

After 1 time constant, voltage a capacitor became Vmax/e = 0.37*V(max). According to the y-axis

in the above graph, 1 volt is equal with 27 mm so 94 mm is equal with 3.48 v = V(max).

V(max) = 3.48 v so V = 0.37*(3.48) = 1.3 v. Also, on the x-axis every 50 ms is equal with 50 mm.

1.3 Volts is correspond with 35 mm on the x-axis. This imply that time is equal with 16 ms. This

time is time constant.  Percent Error = [16 - 14.9 / 14.9 ]*100% = 7.4%

Figure 4: A Schematic of Calculation of Time Constant

Video 1: Discharging of a Capacitor

Video 2: Discharging of a capacitor 

 Inductor Voltage-Current Relations

This lab is similar to above lab. Instead of a capacitor, a inductor is used. A triangular input voltage

with frequency = 1 KHz, amplitude = 1v, and offset = 0v is connected to circuit.

Figure 1: Calculation of Time Constant

R1 = 0.983 KΩ , R2 = 2.17 KΩ , L = 1 mH , Time Constant = L/Req , Time Constant = 10^(-3)/0.677

Time Constant (Theory) = 1.48 μs     (of course, resistance of the inductor is ignored.)

Figure 3: Schematic of a Inductor circuit

 All of quantity such as resistor (R1) voltage difference, total current, and inductor current have

triangular wave. According to, VL(t) = L dI(t)/dt , inductor voltage difference is square.

Figure 3: A Real Graph of a Part of a Real Inductor

After 1 time constant, voltage a inductor grow up to [1-(1/e)]*Vmax = 0.63*V(max). According to

the y-axis in the above graph, 2 mv is equal with 15 mm so 45 mm is equal with 6.0 mv = V(max).

V(max) = 6.0 mv so V = 0.63*(6.0) = 3.8 mv. Also, on the x-axis every 1 μs is equal with 27 mm.

3.8 mv is correspond with 40 mm on the x-axis. This imply that time is equal with 1.48 μs. This

time is time constant.  Percent Error  is zero.