ELECTENG 101 Chap.2 DC Circuit Analysis Methods
DC Circuit Analysis Methods
Select an analysis method from the unknown and the topology. Reduction works only for genuine series or parallel connections. Node voltage handles a small set of essential nodes, superposition separates independent-source contributions, and Thevenin modelling preserves the voltage-current behaviour seen at two terminals. Worked solutions emphasise source suppression, reference directions and terminal checks.
The choice is driven by what must be found: one node potential suggests a node equation, individual source effects suggest superposition, and repeated load changes suggest a terminal equivalent. Dependent sources remain active during source deactivation because their values are controlled by circuit variables.
An open-circuit voltage determines the Thevenin voltage, while resistance looking into the named terminals determines the series resistance. Each reduced model has a boundary of validity, so a terminal equivalent can predict load behaviour without reproducing every internal branch current.
What this chapter covers
- 01
Series and parallel topology
- 02
Voltage and current division
- 03
Node-voltage equations
- 04
Superposition in linear circuits
- 05
Thevenin voltage and resistance
- 06
Load lines and short-circuit current
Worked example · free
Recover a hidden terminal model
- +2Use V = Vth − IRth at both operating points.
- +3Subtracting gives Rth = 3 Ω, then Vth = 13 V.
- +1The short-circuit current is 13/3 = 4.33 A.
Key terms
- Essential node
- A node where three or more branches meet and a node equation can reduce unknowns.
- Superposition
- A linear-circuit method that adds signed responses produced by independent sources acting separately.
- Thevenin voltage
- The open-circuit voltage across the declared terminal pair.
- Thevenin resistance
- The resistance seen looking into the terminals after independent sources are set to zero.
DC Circuit Analysis Methods FAQ
When should I use node voltage?
Use it when a circuit has relatively few essential nodes and branch currents can be written as voltage differences divided by resistance. A source tied to reference can set a node directly. It is especially efficient when many parallel branches meet at the same nodes, because each resistor current follows from one voltage difference instead of becoming a separate unknown.
What happens to sources in superposition?
When one independent source acts, replace other ideal voltage sources with shorts and other ideal current sources with opens. Dependent sources remain because circuit variables control them. This operation imposes zero voltage or zero current; it does not mean deleting every branch that contains a source, and any series or parallel resistance remains connected according to the redrawn topology.
Can I add power by superposition?
No. Add the linear voltage or current contributions first, then calculate power from the total response. Products and squares make power nonlinear. For example, two current contributions that oppose can produce a small total current, so adding their separate I-squared-R values would miss the cross term and overstate the resistor power.
How do I find a Thevenin voltage?
Remove the named load and calculate the voltage across the two exposed terminals with the original independent and dependent sources active. The polarity must match the later equivalent source. Because the load is absent, this is an open-circuit voltage, but other internal branches may still carry current and must remain in the calculation.
When is a test source needed for equivalent resistance?
Use a test voltage or current at the terminals when dependent sources remain and simple series-parallel inspection is insufficient. Deactivate only independent sources, keep the dependent controls operating, solve the resulting terminal voltage-current relation, and take their ratio. This procedure preserves controlled-source behaviour that would disappear if every source symbol were removed.
How can two load measurements reveal a hidden network?
For a linear source, terminal voltage and delivered current lie on the line V equals Vth minus I times Rth. Two distinct operating points determine its slope and intercept. The negative slope gives the internal resistance and the zero-current intercept gives the open-circuit voltage, after which any resistive load can be tested against the same relation.
Exam move
For each circuit, first identify the external quantity being requested. Redraw nodes, test whether reductions are legal, and estimate the likely sign. Solve the same small network once by node voltage and once by superposition to compare references. Practise finding Vth from an open circuit and Rth from a dead-source view, then reconnect several loads and verify the terminal relation V = Vth − IRth.
Create a method-selection card with topology, target unknown and preferred technique on separate rows. Include one circuit that looks series-parallel but contains a branching node, one superposition case with opposing contributions, and one network with a dependent source that requires a test source.
For node equations, inspect the sign pattern before calculating: attached conductances collect on the diagonal and connections to other unknown nodes enter oppositely. After every Thevenin calculation, predict the open-circuit and short-circuit endpoints and confirm the load point lies between them. Finish by explaining aloud why power is evaluated only after contributions are recombined.
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