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.