Network Analysis (a) Determine the currents I1, I2 and I3...

Network Analysis
(a) Determine the currents $I_{1}, I_{2}$ and $I_{3}$ for the electrical network shown in the figure.
(b) How is the result affected when $A$ is changed to
2 volts and $B$ is changed to 6 volts?
(FIGURE CANNOT COPY)

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Key Concepts

Kirchhoff's Laws

Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL) are fundamental in circuit analysis. KCL states that the algebraic sum of currents entering a node equals the sum leaving it, while KVL states that the sum of voltage rises and drops around any closed loop in a circuit is zero. These principles are essential for setting up equations that describe the behavior of electrical networks.

Ohm's Law

Ohm's Law defines the relationship between voltage, current, and resistance in an electrical circuit, stating that the current through a resistor is directly proportional to the voltage across it and inversely proportional to its resistance. This law is critical for relating the calculated voltages and currents in any analysis.

Mesh Analysis

Mesh analysis is a systematic method that uses KVL to solve for unknown currents flowing in the loops (meshes) of a circuit. By writing loop equations, one can effectively determine branch currents in networks that contain multiple loops.

Sensitivity Analysis in Circuits

Sensitivity analysis involves studying how variations in circuit parameters, such as source voltages or resistance values, impact the overall performance (e.g., current distribution). This concept is important when assessing how modifications to elements like voltage sources affect current outcomes in a network.

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