1st order circuits

We started class with learning about series and parallel inductors.  The equivalent inductance of series connected inductors is the sum of the individual inductances. Inductors in series are combined in exactly the same way as resistors in series.

The equivalent inductance of parallel inductors is the reciprocal of the sum of the reciprocals of the individual inductances.  Inductors in parallel are combined in the same way as resistors in paralle.

We did following example of finding value of the equivalent inductance.

1st order circuits:  circuits that contain various combinations of two or three of the passive elements. 

Source free RC circuit:  occurs when its DC source is suddenly disconnected. The energy stored in the capacitor is released to the resistors.  
At time t = 0 , the initial voltage is v(0)=V0
Energy sotred is E - 1/2 CV^2
V(t) = V0 * e^(-t/RC)

Capacitor is fully discharged or charged after five time constants. For every time interval of Taho the voltage is reduced by 36.8% of its previous value regardless of the value of t.

We did following source free circuit example by finding time constant.

LAB: Passive RC Circuit Natural REsponse

In this lab we examine the natural response of a simple RC Circuit. we used manual switching operation and a square wave voltage source to create our circuit's natural response. Following is the set up of our circuit.

Following is the schematic of our RC circuit. We did calculated time constant since we were given R and C values. We estimated intital capacitor voltage and time constant for the circuit as shown below. 

Following is an image of oscilloscope window showing the capacitor voltage response for the circuit shown in previous image where V+ is used as the voltage source. % Error was 20.6% between the calculated values and measured values.

Following is an oscilloscope window showing capacitor voltage response when applying 5V. Percent error was 5.9% . Percent Error is shown in above calculation.

Following is a graph of capacitor voltage response with sinusoidal. Percent Error was 7.56% when comparing with the calculated values.

Error source: Multimeter was not functioning correct at first. some connections were not strong

We did following example of RL circuit with switch been closed for a long time. at t<0 wswitch is closed and the inductor acts as a short circuit to DC.  At t>0 the switch is open and the voltage source is disconnected.

LAB : Passive RL Circuit Natural Response
Professor Mason did this lab as a demo since we ran out of time. Following is he graph of the inductor voltage response. The energy stored in the inductor eventually dissipated in resistor.

Voltage graph generated by the RL circuit.