1. 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

2. 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.

3. 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.

4. 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’

5. A  B  C  D  A = 0 I1R + I1R + I1R - I2R + I1R - I3RF 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

6. Green Circuit - I1R + 4 I2R - 2 I3R = 0F 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

7. Red Circuit - I1R - 2 I2R + 3 I3R = VTF 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

8. 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

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

10. 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

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

12. 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