Circuit Analysis Final Project KEITH PARKER EECT C

1. Resistors – Series & Parallel

For Resistors In Series For Resistors In Series, Resistance Is Cumulative. That is to say R1 + R2 + … R(n) = Rt

For Resistors In Parallel For Any Number Of Equal Value Resistors The total resistance will be equal to the Value of any individual resistor divided by The total number of resistors 2200Ω / 3 resistors = Ω

For Resistors In Parallel For Any Two Unequal Resistors Resistance is given by (R1 * R2) / (R1 + R2)

For Resistors In Parallel For Any Number Of Unequal Resistors Resistance can be found by the reciprocal method 1/((1/R1)+(1/R2)+(1/R3)+(1/R4))

For Parallel and Series Combined For A Circuit With Parallel and Series Combine your resistors. Take the Resistance of the Parallel set by 1/((1/R1)+(1/R2)+(1/R3)+(1/R4)) With that you may think of it as one Resistor. Now its in series with your First resistor. Add for your total resistance. R R5 = Rt

2. Resistor Network

Resistance Resistance is found by the reciprocal Method for the parallel part, then Adding them to the series part of the Circuit Rt = R(789) = R6 + R10

Branch Currents and Voltages Currents were found using Ohm’s law. I = VR For current total it was I = 9v / Ohms For the branches there were 4 branches so each Drop should be Itotal / 4 to get 213uA. So each Branch total had 213uA taken from it. For the opposite branches the totals were the same. In parallel current in = current out. For voltages, voltage drop across the series resistor was Taken as V = (R5 / Rt ) * Vt On the parallel part voltage is constant.

3. Thevenin Resistance / Voltage of a Resistor Network

RL is calculated as the Resistance of the Load In this case RL = 100 Ω Vth is calculated as Va – Vb Va = R12 * Itotal Vb = ((R2/(R1+R2))*Vtotal) - ((R45/(R3+R45))*Vtotal) Vth = 4.5V Rth is the resistance looking back into the Circuit with the power source shorted out Rth = 10Ω

4. Multiple Capacitors in Parallel and Series

Capacitance in Parallel is C1 + C2 + C3 = Ctotal Capacitance in Series is 1/(1/C1)+(1/C2)+(1/C3) = Ctotal Multisim had to have an expression added to the Single Frequency AC Analysis to allow it to measure capacitance. The expression is as follows. Vout1 : 1/((abs(imag(V(vout1)/I(R1))))*1000*2*pi) Vout2 : 1/((abs(imag(V(vout2)/I(R1))))*1000*2*pi)

5. RC Circuits

Time Constant is R * C 1000 Ω* 10uF =.001 For RC as a function of time For Vc Vs*(1-EXP(-Time/TC)) To Graph RC as a function of time for Vc Vs =1 2  = 2.0E-3 R =1.0E+3 3  = 3.0E-3 C =1.0E-6 4  = 4.0E-3  = 1.0E-3 5  = 5.0E-3 Deta T =100.0E-6 TimeVc 000.0E E-695.2E-3 Time constant is calculated as R * C200.0E E E E-3 R1.00E+03Ω400.0E E-3 C1.00E-05uF500.0E E-3 RC1.00E E E E E-3 It takes 5 time constants to fully charge800.0E E E E-3 RC22.00E-021.0E E-3 RC33.00E-02 RC44.00E-02 RC55.00E-02

RC As A Function Of Time - Multisim

Xc is calculated as Xc = (1/(2PI*Freqency*Capacitance) Xc As A Function Of Frequency

Xc As A Function Of Frequency - Multisim

6. Inductors In Series And Parallel

Inductors in series are additive. L1 + L2 + L3 = Ltotal Inductors in parallel are reciprocal. 1 / ((1/L1) + (1/L2) + (1/L3)) = Ltotal

7. Simple RL Circuit

The Time Constant is calculated as L/R For this circuit, 1mH / 1kΩ

RL Time The current out is calculated as (R/L)*(1-EXP(-R*Time/(L/R)

RL Time - Multisim

Xl As A Function Of Frequency Xl is calculated as Xl = 2*PI*Frequency*L

Xl Multisim