Impedance an d AC analysis I

The purpose of the first part is to investigate a real-world inductor which is equivalent to connect with RL and L in series, so the impedance Z can be determined as ZL = RL + jwL and determine the inductance by looking for the ratio of magnitude of the terminal voltage and current phasors by following circuit.

Next, set the RMS voltage of the function generator with 20KHz, then  device the circuit and  record the reading from the multimeter and ammeter

V in,rms =4.53V

I in,rms =88mA

The reading is different from the FB display because there is some internal resistance due to the function generator.

Next, make computations:

|Z|=|V|/|I| = 4.52/88mA=51.36ohm

Z=R_ext+R_L+jwL

|Z|=sqrt((R_ext+R_L)^2+(wL)^2))

w=2πf==125664 rad/s

Since we know the value of Z, R_ext, R_L and w

we will need to find L, which is about 0.4mH

Investigating a Series RLC circuit:

Data

Scope measurement at 20.97 kHz.

Vp-p,ch1 = 23.08 V

Vp-p,ch2 = 19.49 V

Δ t = 19.46 us

The phase difference = Δ t * f *360 degree = 19.46 us* 20.97kHz * 360 degree = 146 degrees

Then, use DDM to measure the voltage and current at different frequency

Question:

1. Why is the input current that largest at 20.0kHz(12.7K)?

The input current is largest because the impedance of the element is the smallest

2. Calculate the theoretical voltage phasor across the real inductor at 20.97KHz (use the DMM measurement value as the source voltage phasor magnitude). Compare this with the scope measurements. Convert the scope measurement to RMS for comparison purposes.

Theoretical: (23.08/(2sqrt(2))*2pi*20.97*1000*0.4*10^-3/(68.5+3.4)=5.98V

Experimental: 19.49/(2sqrt(2))=6.89

% Error: (6.89-5.98)/5.98=15.2%

3. Does the circuit look more capacitive or inductive at frequencies below 20kHZ?

capacitive

4. Does the circuit look more capacitive or inductive at frequencies above 20kHZ?

inductive