In applying Kirchhoff's laws to the circuit shown in Fig....

In applying Kirchhoff's laws to the circuit shown in Fig. 16.15 following equations are found. Determine the indicated currents $(\text { in } \mathrm{A})$.
$$\begin{aligned}
I_{A}+I_{B}+I_{C} &=0 \\
2 I_{A}-5 I_{B} &=6 \\
5 I_{B}-I_{C} &=-3
\end{aligned}$$
(FIGURE CAN'T COPY)

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Key Concepts

Kirchhoff's Current Law (KCL)

Kirchhoff's Current Law states that at any junction (node) in an electrical circuit, the sum of currents entering the node is equal to the sum of currents leaving the node. This law is based on the conservation of electric charge and is fundamental in setting up equations that describe current flow in complex circuits.

Kirchhoff's Voltage Law (KVL)

Kirchhoff's Voltage Law asserts that the sum of the electrical potential differences (voltages) around any closed loop in a circuit must equal zero. This principle is derived from the conservation of energy and is used to relate voltage drops and rises in various elements of the circuit via loop equations.

System of Linear Equations

In circuit analysis, applying Kirchhoff's laws typically results in a system of linear equations that describe the relationships between currents and voltages in the circuit. Solving these equations using algebraic methods like substitution or elimination allows one to determine the unknown electrical quantities, making it a crucial step in analyzing electrical networks.

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