Created for CVCA Physics By Dick Heckathorn 22 March 2K+5 Figure 8 Resistors Created for CVCA Physics By Dick Heckathorn 22 March 2K+5

Kirchhoff’s Current Law At any junction point in an electric circuit, the total electric current into the junction is equal to the total electric current out of the junction.

Kirchhoff’s Voltage Law Around any complete path through an electric circuit, the sum of the increases in electric potential is equal to the sum of the decreases in electric potential.

What is RT or REquivalent? Each resistance has value ‘R’ Figure 8 Resistors C F B I1 I2 I3 I1 I2 I3 I1 I2 I3 I1 I2 A I3 D I3 E I3 I3 VT What is RT or REquivalent? Each resistance has value ‘R’

A  B  C  D  A = 0 I1R + I1R + I1R - I2R + I1R - I3R F B I1 I2 I3 I1 I2 I3 I1 I2 I3 I1 I2 A I3 D I3 E I3 I3 VT Blue Circuit A  B  C  D  A = 0 I1R + I1R + I1R - I2R + I1R - I3R 4 I1R - I2R - I3R = 0 #1

Green Circuit - I1R + 4 I2R - 2 I3R = 0 F B I1 I2 I3 I1 I2 I3 I1 I2 I3 I1 I2 A I3 D I3 E I3 I3 VT Green Circuit C  F  E  D  C + I2R + I2R - I3R + I2R - I3R + I2R -I1R = 0 - I1R + 4 I2R - 2 I3R = 0 #2

Red Circuit - I1R - 2 I2R + 3 I3R = VT F B I1 I2 I3 I1 I2 I3 I1 I2 I3 I1 I2 A I3 D I3 E I3 I3 VT V Red Circuit A  D  E  F  A I3R - I1R + I3R - I2R + I3R - I2R = VT - I1R - 2 I2R + 3 I3R = VT #3

3 Equations with 3 Unknowns 4 I1R - I2R - I3R = 0 #1 - I1R + 4 I2R - 2 I3R = 0 #2 - I1R - 2 I2R + 3 I3R = VT #3

Now for the analysis Combine Equations 1 & 3 # 1 4 I1R - I2R - I3R = 0 [ - ] x4 # 3 I1R - 2 I2R + 3 I3R = V # 3 - 4 I1R - 8 I2R + 12 I3R = 4V # 1 4 I1R - I2R - I3R = 0 # 1&3 - 9 I2R + 11 I3R = 4V

Combine Equations 2 & 3 # 2 - I1R + 4 I2R - 2 I3R = 0 # 3 [ ] x-1 - I1R - 2 I2R + 3 I3R = VT # 3 + I1R + 2 I2R - 3 I3R = - VT # 2 - I1R + 4 I2R - 2 I3R = 0 # 2&3 + 6 I2R - 5 I3R = - VT

Continued analysis # 1&3 - 9 I2R + 11 I3R = 4 VT ] x2 ] x3 # 2&3

Continued analysis 7 I3R = 5 VT VT = IT RT 7 I3R = 5 IT RT I3 = IT 7 R = 5 RT RT = 7/5 R R = 10 Ω RT = 14 Ω