Question

For the circuit below (a) Define the currents in each part of the circuit (b) Write the equation for Kirchhoff’s junction rule. (c) Write Kirchhoff’s equation for the left circuit loop (d) Write Kirchhoff’s equation for the right circuit loop. (e) Show the complete solution to the three equations for the currents in the various parts of the circuit. 4Ω, 18 V, 6 V, 6 Ω, 8Ω.

Answer 1

b)

$I_1-I_2-I_3=0$

c)

$4\cdot I_1+6\cdot I_2=18-6$

d)

$8\cdot I_3-6\cdot I_2=6$

e)

$I_1-I_2-I_3=0$

$4\cdot I_1+6\cdot I_2+0=12$

$0-6\cdot I_2+8\cdot I_3=6$

$\Delta=\begin{vmatrix} 1 & -1&-1 \\ 4 & 6 & 0 \\ 0 & -6 & 8 \end{vmatrix}=104$

$\Delta_1=\begin{vmatrix} 0 & -1&-1 \\ 12 & 6 & 0 \\ 6 & -6 & 8 \end{vmatrix}=204$

$\Delta_2=\begin{vmatrix} 1 & 0&-1 \\ 4 & 12 & 0 \\ 0 & 6 & 8 \end{vmatrix}=72$

$\Delta_3=\begin{vmatrix} 1 & -1&0 \\ 4 & 6 & 12 \\ 0 & -6 & 6 \end{vmatrix}=132$

$I_1=\frac{\Delta_1}{\Delta}=\frac{204}{104}=\frac{51}{26}\approx 1.96 A$

$I_2=\frac{\Delta_2}{\Delta}=\frac{72}{104}=\frac{9}{13}\approx 0.69 A$

$I_3=\frac{\Delta_3}{\Delta}=\frac{132}{104}=\frac{33}{26}\approx 1.27 A$

a)