DC Circuits

About this book

DC Circuits by Chad Davis builds direct-current analysis through three modules: resistor networks, advanced resistive methods, and circuits containing capacitors and inductors. This guide follows the first edition dated August 8, 2016 and summarizes its seventeen instructional sections plus the appendix. A circuit diagram is a mathematical model with explicit reference choices. Derive relationships before substituting numbers, check energy and limiting behaviour, and distinguish a transient from the long-time state. Numerical agreement is strongest when supported by a second method and an explanation of the physical result.

Chapter-by-chapter summaries

1.1. Definitions and basic quantities

Charge, current, voltage, resistance, power, and energy describe different aspects of a circuit. Reference arrows and polarities define signs; a negative answer can indicate direction rather than an error. Keep units and the passive-sign convention consistent. Explain how power differs from accumulated energy. Start with a simple source-load model and check conservation. The definitions become practical tools when every symbol is attached to a physical or diagrammatic meaning.

1.2. Series and parallel resistors

Series elements share a current only when the connection provides the required single path; parallel elements share the same two nodes. Appearance on a drawing does not establish either relationship. Redraw nodes before combining components. Equivalent resistance preserves a terminal relationship rather than the internal behaviour of every original resistor. Check whether the equivalent lies in a plausible range and recover individual currents or voltages when the problem asks about internal elements.

1.3. KVL and voltage division

Kirchhoff’s voltage law applies a consistent loop accounting of voltage changes. Voltage division follows from the structure of a series path, not from the mere presence of several resistors. Identify whether loading changes that structure. Walk a loop with explicit sign choices and check the sum. A divider formula becomes reliable when its derivation is understood, allowing a reader to recognize when a superficially similar circuit does not satisfy its assumptions.

1.4. KCL and current division

Kirchhoff’s current law balances flow at nodes, while current division applies to suitable parallel branches. Assign reference currents and use algebra consistently rather than changing signs to match an anticipated answer. For two branches, relate larger resistance to smaller current under a common voltage. With more branches, conductance provides a useful representation. Check that branch currents sum to the entering current and distinguish node identity from the physical spacing of wires on a drawing.

2.1. Source transformations

Thevenin and Norton forms describe equivalent terminal behaviour through a voltage source with series resistance or a current source with parallel resistance. Transform the complete source-resistance combination, preserving the terminals and polarity. Internal currents need not remain identical. Explain what a connected load experiences before treating two drawings as equivalent. A transformation is an analytical representation with defined conditions, not a claim that all physical sources are interchangeable internally.

2.2. Approximate transformations

Adding a virtual resistance can support an approximation when an ideal source prevents a convenient direct transformation. The approximation introduces an assumption that must be checked against the surrounding circuit and desired accuracy. Compare the resulting answer with a limiting case or a direct formulation. Do not present an approximation as an exact identity merely because the numbers are close in one example. State which ratio or parameter makes the neglected influence small.

2.3. Mesh and loop analysis

Loop equations organize unknown currents through voltage-law relationships, with matrix form supporting larger systems. Choose independent loops and account for shared elements consistently. A resistor between meshes carries a combination of mesh currents, not necessarily one mesh variable alone. Solve a small system by hand and compare the matrix result. Independence and sign consistency matter more than the visual neatness of the chosen loops.

2.4. Nodal analysis

Node voltages relative to a reference organize current-law equations. Choose a reference, label independent node potentials, and express branch currents through differences. Sources may require special handling within the method. Compare a nodal solution with loop analysis for the same circuit. Different reference choices change numerical node potentials without changing physical voltage differences. This distinction helps identify an apparent disagreement that is only a change of coordinates.

2.5. Superposition

In a linear model, contributions from independent sources can be combined while applying the correct source-deactivation rules. Dependent sources remain tied to their controlling quantities. Superposition applies directly to voltage and current, not generally to power because power is nonlinear in those quantities. Calculate contributions with fixed references and add algebraically. Check the combined result in the original circuit rather than assuming each partial circuit has an independently meaningful physical operating state.

2.6. Thevenin and Norton equivalents

Equivalent circuits summarize a network at selected terminals, making changing loads easier to analyze. Determine the relevant terminal quantities and equivalent resistance using a method suitable for the sources present. Preserve dependent-source relationships where applicable. Compare the equivalent and original network with two loads to test the intended relationship. The simplification answers terminal questions; it does not reveal every original component’s internal power or current without further analysis.

3.1. Capacitors

Capacitance connects charge and voltage, while current depends on voltage change. Stored energy and initial voltage introduce behaviour absent from a purely resistive model. A capacitor’s voltage cannot change instantaneously under the ordinary finite-current idealization. State the initial condition and reference polarity. Compare its transient role with its long-time DC representation, remembering that the latter is a limiting result rather than a description of every moment after switching.

3.2. Inductors

Inductance connects magnetic energy with current, and voltage depends on current change. Initial current is part of the state. Under an ordinary finite-voltage model, inductor current cannot jump arbitrarily. Compare short-time behaviour with long-time DC behaviour and identify what the chosen idealization neglects. Keep the passive-sign convention visible in derivative relationships. This prevents a memorized steady-state shortcut from replacing the actual dynamic question.

3.3. Combining inductors

Series and parallel inductances can be reduced under the assumptions represented by the circuit, including whether coupling is excluded. Verify topology before applying a combination rule. Explain how the equivalent relates current change to terminal voltage. Where initial states matter, check that the simplified representation retains the information needed for the problem. A numerical equivalent is useful only when it preserves the relationship actually being analyzed.

3.4. Combining capacitors

Capacitor combination rules differ from the corresponding resistor patterns because charge and voltage organize differently. Derive a two-element case to understand why. Check that an equivalent remains physically plausible. Initial charge or voltage can matter when connections change, so a static equivalent alone may not specify the complete transient. Distinguish simplifying a fixed network from assuming that an abrupt reconnection has no additional consequences.

3.5. RC and RL transients

First-order responses connect an initial state, a final state, and a time constant. Determine each from the actual switched configuration rather than assigning them from a familiar diagram. A time constant sets the exponential scale, not an exact completion time. Verify the response at zero and at long times, then compare its derivative with the governing equation. The same mathematical shape describes different physical quantities depending on the circuit and output selected.

3.6. DC steady state

Long-time ideal representations of capacitors and inductors can simplify RC, RL, and RLC networks when a suitable steady state exists. Check the topology and source conditions before replacing elements. Steady-state analysis does not describe initial stored energy or all switching behaviour. Compare the limiting result with a transient model and account for energy storage. A shortcut is justified by a limiting argument, not by the presence of a DC label alone.

3.7. Introduction to passive filters

Capacitors and inductors introduce frequency-dependent behaviour that links DC foundations with later AC study. Identify input and output terminals and explain how component relationships change with variation rate. Compare low- and high-frequency limits conceptually before deriving a complete response. Loading and source resistance matter. The section introduces a new application of existing models rather than a collection of unrelated filter names.

Appendix: dependent sources and transform examples

Dependent-source and Laplace-transform examples extend the core methods. Keep controlling variables defined and distinguish independent-source deactivation from removing a dependent relationship. Transform methods also require initial-condition accounting. Use the appendix after the corresponding circuit principles are clear, then compare its result with time-domain reasoning for a simple case. This makes the advanced notation a compact representation of understood relationships rather than a substitute for them.

Study instructions

1. Redraw and label nodes, terminals, references, and initial conditions before solving.
2. Use two methods on selected examples and explain equivalence rather than only matching numbers.
3. Check power balance, units, and zero- or long-time limits.
4. Maintain a distinction sheet for exact equivalents, approximations, transient models, and steady-state shortcuts.

Questions for reflection

• What does a terminal equivalent preserve and what can it hide?
• Why is power not generally superposed?
• When does a steady-state shortcut fail to answer a switching question?

Sources and coverage

This original reading guide follows the linked source edition’s chapter, module, unit, or lesson structure. Consult the source for full arguments, cases, worked examples, exercises, illustrations, and references. First edition, August 8, 2016. All seventeen main instructional sections across three modules are summarized, together with the appendix. Read the source edition.