Parallel RLC Circuit Step Response

Purpose: 

Pre-lab:

This lab is similar to the previous lab except it is constructed in PARALLEL with an extra Resistor. 

In this case, we combined R1 and R2 into an equivalent R.

In this case, we also found that ω>α -> underdamped case.

For theoretical period T, we got 0.6433ms and experimental period T based on the graph below, period T=0.6273ms.

Finally, here is the picture of our circuit

Series RLC Circuit Step Response

Purpose: 

Pre-lab:

With the circuit provided above and we calculated the V(out)/V(in)

As we calculated: α < ω (631.068 < 85438.884), and that gave us the UNDERDAMP case. The V_in provided by Digital Analog was 5V, and at steady state, we measured V(infinity)=5.04V. The ratio of V_out/V_in = 1.008. Based on information given in lab, we calculated our period T=4ms

Picture of our steady state.

Graph of an underdamped case.

Here is a picture of our circuit.

Passive RL Circuit Natural Response

Purpose:

Prelab: 

The requirement of this lab is almost similar to the previous lab which is RC Circuit Natural Response.
We calculate V(t) of Inductor at t>0 and then calculate the value of Tau theoretically and experimentally.

The i_L(t) = 0.05e^(-t/Tau), theoretical Tau = L/R2 = 2.128 x 10^(-5) s.
Then value of V_L(t) can be calculated by Ldi/dt. V_L(t)= (-0.05/(2.128x10^(-5)))e^(-t/Tau)

We use the same method as previous lab which is choosing V1,V2 and delta t to find experimental Tau.
The value of experimental Tau = 2.017 x 10^(-5) s
%Diff= 5.5 %
In this experiment, the time constant Tau is L/R, but R is only R2 since we unplug R1.

Here is the picture of our result by using Digital Analog.

Passive RC Circuit Natural Response

Purpose:

Prelab:

We constructed the circuit above, and calculate value of Vc(t), Tau at t>0

Value of Vc(0) = 3.221V through Vc(t) = 3.221e ^(-t/Tau)
Our theoretical value of Tau is 0.04752s compared to experimental value of Tau is 0.0491s
% Diff  = 3.21%
We find the value of experimental value of Tau by choosing value of V1 = 3.221V and V2=1.005V, then record their delta t and plug in to the equation of Vc(t) to find Tau.

Here is the picture of our circuit constructed.

This makes sense because when we unplug (like a switch in the description of the lab), V of capacitor drops down exponentially to 0.

Leakage Currents and Electrolytic Capacitors

Purpose:

We will construct a circuit like picture below:

The polarity of the electrolytic capacitor is important, it is not symmetric like other capacitors. When we change the polarity, the behavior of capacitor can be changed as such. The longer lead will be anode(+), and the shorter lead will be cathode(-). 

We also use R=100Ω, C=10μF connected in series, and power supply will be 5V. We will "disconnect" and "reconnect" the power supply to observe the behavior of capacitor when charging and uncharging. 

Tau = RC= 100 * 10 * 10^(-6) = 0.001s

In order to fully charged, it will take 5T = 0.005s. In our experiment, time for capacitor to be fully charged happened quickly as well.

But when it comes to discharging, our experiment result was completely off. The reason for that would be the huge internal resistance in the circuit. Since we learned that the leakage happen when value of resistor should be around 500MΩ while we only have 100Ω. 

Here is the picture of our circuit.

Capacitor Voltage-Current Relations

Purpose: In this lab, we will measure the voltage and current across a capacitor to see the relationship between them.

Pre-lab:
By measuring the voltage across the capacitor, we can easily calculate the current across it by using: Ic=Vr/R since resistor and capacitor are connected in series, so they have the same current pass through.

 Triangular of Vr and Vc

 Sinusoidal of Vr and Vc

 Picture of our circuit.

Triangular of Vr and Vc

Summing Amplifier

Purpose:

Pre-lab: Calculate Vout based on 2 Vins (Va and Vb) with Vb=1, Va=-4,-2,-1,0,1,2,3 and 5V.

R1=1.77kΩ, R2=1.19kΩ, R3=1.29kΩ

At 5V, it reaches saturation because value of Vexp vs Vtheo is off.