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