--- author: Akbar Rahman date: \today title: MMME2051 // Kirchhoff's Current Law, Voltage Law tags: [ kirchhoff, kcl, kvl ] uuid: 88e2eb6a-7f6a-4ea0-9850-81305028e7b5 lecture_slides: ./lecture_slides/MMME2051EMD_Lecture2A.pdf --- # Application of Kirchhoff's Current/Voltage Laws (KCL, KVL) (lecture slides 14-21)  1. Identify all the loops in the circuit and assign each loop a "loop current" variable:  1. Identify "branch current" values (apply KCL)  1. Apply KVL to each loop: Loop 1: $10 - 2 - V_1 - V_2 = 0$ Loop 2: $V_2 - V_4 = 0$ Loop 3: $V_4 - V_3 - V_5 = 0$  1. Apply Ohm's Law to KVL Loop 1 (origin at node A): \begin{align*} 0 &= 10 - 2 - V_1 - V_2 \\ &= 8 - I_1R_1 - (I_1-I_2)R_2 = 0 \\ 8 &= I_1(R_1+R+2) - I_2R_2 \\ &= 6I_1 - I_2 \end{align*} Loop 2 (origin at node B): \begin{align*} 0 &= V_2 - v_4 \\ &= (I_1-I_2)R_2 - (I_2-I_3)R_4 \\ &= I_1 - 3I_2 + 2I_3 \end{align*} Loop 3 (origin at node C): \begin{align*} 0 &= V_4 - V_3 - V_5 \\ &= (I_2-I_3)R_4 - I_3R_3 - I_3R_5 \\ &= 2I_2 - 5I_3 \end{align*}