R11kΩ

R22.2kΩ

R33.3kΩ

XMM1

Resistors in Series

Formula:RT = R1 + R2 + R3…

RT = 6.5E+3 KΩ

Verified in MultiSim:

A B

123

Resistors in Parallel

Formula:

654

T

R1

R1

R1

1R

R4 = 4700 ΩR5 = 3300 ΩR6 = 10000 ΩRT = =1/((1/H4)+(1/H5)+(1/H6)) KΩ

RT = 1.624E+3 KΩ

R44.7kΩ

R53.3kΩ

R610kΩ

XMM1

Verified in MultiSim

G H456

Resistors in Parallel(continued)

R11kΩ

R21kΩ

R31kΩ

R41kΩ

XMM1

Formula for Multiple Equal Resistors: Formula for two Unequal Resistors:

R1 = 1000 ΩR2 = 1000 ΩR3 = 1000 ΩR4 = 1000 ΩRT = 250 Ω

RT = =B1/4 Ω

R1 = 1000 ΩR2 = 5000 ΩRT = 833.33 Ω

Verified by MultiSim

RT = =(B1*B2)/(B1+B2) Ω

R11kΩ

R25kΩ

XMM2

A B1234

A B12

Resistors in Series/Parallel

R1 = 1000 ΩR2 = 2200 ΩR3 = 3300 ΩR4 = 4700 ΩR5 = 10000 Ω

R234 = =1/((1/B3)+(1/B4)+(1/B5)) KΩRT = =B2+B7+B6 KΩ

RT = 12.031E+3 KΩ

R1

1kΩ

R22.2kΩ

R33.3kΩ

R44.7kΩ

R5

10kΩ

XMM1

R2a2.2kΩ

R3a3.3kΩ

R4a4.7kΩ

XMM2

R1a

1kΩ

R5a

10kΩ

XMM3R2341.031kΩ

Formula:First, use parallel formula, then use series formula.

Verified in MultiSim

A B234567

R1a

25Ω

R5a

25Ω

R2a100Ω

R3a100Ω

XMM3

V2100 V

R1b

25Ω

R5b

25Ω

R2b100Ω

R3b100Ω

XMM2

R1c

25Ω

R5c

25Ω

R2c100Ω

R3c100Ω

XMM1

VTH

RTH

Thevenin

RT

V = 100 VRT = =(B5*B6)/(B5+B6)+B4+B8 Ω (with RL removed)IT = =B1/B2 AR1 = 25 ΩR2 = 100 ΩR3 = 100 ΩR4(RL) = 25 ΩR5 = 25 ΩR23 = =(B5*B6)/(B5+B6) ΩR15 = =B4+B8 ΩRTH = =(B9*B10)/(B9+B10) ΩER1 = =B3*B4 VER5 = =B3*B8 VVTH = =(B3/2)*B2 V

IL = =B14/(B11+B7) A

VL = =B7/(B7+B11)*B14 V

Formulas for IL and VL:VTH

RTH + RL

IL =

RL

RL + RTH

VL = X VTH

Verified in MultiSim

A B123456789

10111213141516

IT = 1 AR1 = 25 ΩR2 = 100 ΩR3 = 100 ΩR4(RL) = 25 ΩR5 = 25 ΩR23 = 50 ΩR15 = 50 ΩRTH = 25 Ω

ER1 = 25 VER5 = 25 VVTH = 50 V

IL = 1 A

VL = 25 V

RT = 100 Ω

V = 9RT = =C4+C9+C8IT = =C1/C2

A B C D

Powers and Currents

VB

VC

1 V = 9 V2 RT = 12.031E+3 KΩ3 IT = 748.095E-6 µA4 R1 = 1.000E+3 KΩ5 R2 = 2.200E+3 KΩ6 R3 = 3.300E+3 KΩ7 R4 = 4.700E+3 KΩ8 R5 = 10.000E+3 KΩ9 R234 = 1.031E+3 KΩ10 IR1 = 748.095E-6 µA11 IR2 = 350.436E-6 µA12 IR3 = 233.624E-6 µA13 IR4 = 164.034E-6 µA14 IR5 = 748.095E-6 µA15 VB = 8.252E+0 V16 VC = 7.481E+0 V17 PR1 = 559.645E-6 uW18 PR2 = 270.172E-6 uW19 PR3 = 180.115E-6 uW20 PR4 = 126.464E-6 uW21 PR5 = 5.596E-3 mW22 PT = 6.733E-3 mW

IR1 = =(C1-C15)/C4 µAIR2 = =(C15-C16)/C5 µAIR3 = =(C15-C16)/C6 µAIR4 = =(C15-C16)/C7 µAIR5 = =C16/C8 µAVB = =9-((C1*C4)/C2) VVC = =C15-((C1*C9)/C2) V

PR1 = =C10^2*C4 uWPR2 = =C11^2*C5 uWPR3 = =C12^2*C6 uWPR4 = =C13^2*C7 uWPR5 = =C14^2*C8 mW

PT = =C1*C3 mW

C1.1µF

C2.47µF

C31µF

V1

1 Vpk 1kHz 0°

Probe1

C3a1µF

C2a.47µF

C1a.1µF

V3

1 Vpk 1kHz 0°

Probe2

In Series

In Parallel

C1 = 0.1 µFC2 = 0.47 µFC3 = 1 µFCT = 76.175E-3 µFCT = =1/((1/B2)+(1/B3)+(1/B4)) µF

C1a = 0.1 µFC2a = 0.47 µFC3a = 1 µFCTa = 1.57E+0 µFCTa = =E2+E3+E4 µF

Verified in MultiSim

Capacitors

A B234

D E234

Xc as a Function of FrequencyParallel Capacitors

freq Vin Vout(VA) DB1 1 1 0

10 1 1 020 1 0.984 -0.14009803130 1 0.968 -0.28249285440 1 0.936 -0.57448302550 1 0.904 -0.8766313960 1 0.864 -1.2697251570 1 0.824 -1.68145576680 1 0.784 -2.11367874690 1 0.752 -2.475643188

100 1 0.712 -2.950400127110 1 0.688 -3.248231235120 1 0.656 -3.661923212130 1 0.624 -4.096308206140 1 0.592 -4.553565866150 1 0.560 -5.03623946160 1 0.544 -5.288022006170 1 0.512 -5.81460078175 1 0.504 -5.951389271177 1 0.500 -6.020599913180 1 0.496 -6.09036647190 1 0.480 -6.375175252200 1 0.464 -6.669640389300 1 0.328 -9.682523126400 1 0.256 -11.83520069500 1 0.208 -13.6387333600 1 0.176 -15.08974664700 1 0.160 -15.91760035800 1 0.144 -16.83275016900 1 0.128 -17.85580061

1000 1 0.112 -19.015639552000 1 0.064 -23.876400523000 1 0.048 -26.375175254000 1 0.032 -29.897000435000 1 0.032 -29.89700043

10000 1 0.016 -35.91760035

Parallel Capacitors:As frequency increases, Capacitance decreases.

Xc as a Function of FrequencySeries Capacitors

freq Vin Va DB1 1 1 0

10 1 1 020 1 1 030 1 1 040 1 1 050 1 1 060 1 1 070 1 1 080 1 1 090 1 1 0

100 1 1 01000 1 0.9 -0.915152000 1 0.76 -2.383733000 1 0.6 -4.436974000 1 0.5 -6.02065000 1 0.44 -7.130956000 1 0.38 -8.404337000 1 0.34 -9.370428000 1 0.3 -10.45769000 1 0.28 -11.0568

10000 1 0.26 -11.700520000 1 0.18 -14.894530000 1 0.14 -17.077440000 1 0.14 -17.077450000 1 0.12 -18.416460000 1 0.12 -18.416470000 1 0.12 -18.416480000 1 0.12 -18.416490000 1 0.1 -20

100000 1 0.1 -201000000 1 0.1 -20

Series Capacitors:As frequency increases, Capacitance decreases.

Xc as Function of Frequency

C11µF

R2

1kΩ

V1

0 V 1 V 10ms 20ms

XSC2

A B

Ext Trig+

+

_

_ + _

Va

Xc Time Constant

Inductors: Series & Parallel

V2

1 Vpk 1kHz 0°

L2.47H

L3.1H

L11H

R1.01Ω V4

1 Vpk 1kHz 0° L4

1HL5.47H

L6.1H

R2.01Ω

R3.01Ω

R4.01Ω

LT = =B1+B2+B3 H LT = =1/((1/B1)+(1/B2)+(1/B3)) H

Series Parallel

Verified in MultiSim

L4 = 1 HL5 = 0.47 HL6 = 0.1 HLT = 76.175E-3 H

(Small resistor added in simulation to keep circuit from “shorting” out.)

A B A B123

123

L2.47H

L3.1H

L11H

R1

1kΩVa

V2

0 V 1 V 10ms 20ms

VinProbe1

V: I:

XL as a Function of Frequency

L5.47H

L6.1H

L71H

R3

1kΩ

V3

0 V 1 V 10ms 20ms

Vin_1R40.01Ω

R50.01Ω

R60.01Ω

V_a

Series

Parallel

XL Time Constants

XCP1100 mV/mA

V2

0 V 1 V 10ms 20ms

R1

100Ω

L1100mH

XSC1

A B

Ext Trig+

+

_

_ + _

Vb