E3 Analysis of DC Circuits

Topic

Direct-current (DC) circuit analysis systematizes the calculation of voltages and currents in networks of interconnected components by relying on two conservation principles. Kirchhoff's current law states that the sum of all currents entering and leaving a node must be zero; this is simply an expression of the charge conservation principle established in the first model of this catalog—namely, that charge neither accumulates nor disappears at a connection point. Kirchhoff's voltage law states that the sum of potential differences along any closed path in a circuit must be zero, representing the application of energy conservation to a circuit.

Based on these two laws, nodal analysis transforms any circuit into a system of equations that, when solved, yields all the circuit's voltages simultaneously. Thévenin's theorem takes this simplification a step further: any linear network—regardless of internal complexity—can be replaced (when viewed from two terminals) by a single voltage source in series with a single equivalent resistor, greatly simplifying the analysis of circuits with multiple sources. The superposition principle, applicable to linear circuits, states that the response to multiple sources acting simultaneously is equal to the sum of the responses produced by each source individually while the others are turned off.

The voltage divider—consisting of two resistors in series that split an input voltage in proportion to their values—is the simplest and most ubiquitous circuit in all of electronics among those that can be constructed using these laws.

Thus, this module, which begins with two conservation laws, concludes by demonstrating that these laws are not merely calculation tools but a guarantee that any circuit—no matter how complex it appears—can be reduced (via nodal analysis, Thévenin's theorem, or superposition) to something as simple as the voltage divider itself, with which this model concludes.

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