Kirchhoff's Laws
Table of Contents
1. Kirchhoff's Voltage Law (KVL)
Kirchhoff's voltage law states that the sum of all voltages around a loop must be zero. The convention is that going from positive to negative terminals yields a positive voltage drop, so we add voltage, whereas going from negative to positive terminals yields a negative voltage drop, so we subtract voltage.
2. Kirchhoff's Current Law (KCL)
Kirchhoff's current law states that the algebraic sum of all currents either entering or leaving a node is zero. In other words, the total amount of current entering a node must equal the total amount of current leaving.
Example: Circuit analysis
Consider the following circuit:
We want to find \(I_1\), \(I_2\), and \(I_3\). By KCL, we have:
\begin{align} I_1 &= I_2 + I_3 \notag \\ I_3 &= I_1 - I_2 \notag \end{align}Then, using KVL on \(L_1\):
\begin{align} 5I_1 + 10I_3 &= 10 \notag \\ 5I_1 + 10I_1 - 10I_2 &= 10 \notag \\ 3I_1 - 2I_2 &= 2 \notag \end{align}Then, using KVL on \(L_2\):
\begin{align} -10I_3 + 5I_2 + 5I_2 &= 0 \notag \\ 10I_2 - 10I_1 + 10I_2 &= 0 \notag \\ 2I_2 - I_1 &= 0 \notag \end{align}Finally, combining with the previous equations, we get our answers:
\begin{align} \boxed{I_1 = 1 \text{A}, \: I_2 = 0.5 \text{A}, \: I_3 = 0.5 \text{A}} \notag \end{align}