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Network Analysis

DC Circuit Analysis

DC circuit analysis helps you find steady voltages, currents, and power in a circuit where current direction does not keep changing. The main skill is to choose the right method, simplify the network, and solve it step by step.

01

Basic Analysis

Basic DC analysis starts by reading the circuit with Ohm's Law, KCL, and KVL together.

Concept Breakdown

  • Ohm's Law connects voltage, current, and resistance in each element.
  • KCL checks how current splits or combines at a node.
  • KVL checks how voltage rises and drops around a loop.
  • This approach works best when the circuit is small and easy to trace.

Formula

V = IR

  • V is the voltage across a resistor.
  • I is the current through that resistor.
  • R is the resistance limiting the current.

Step-by-Step Method

  1. 1Mark known source and resistor values.
  2. 2Choose current directions and voltage polarities.
  3. 3Apply Ohm's Law where voltage and resistance are known.
  4. 4Use KCL at junctions and KVL around loops.
  5. 5Solve the equations and check if signs make sense.

Key Idea

Small DC circuits can often be solved by carefully combining Ohm's Law, KCL, and KVL.

Animation Idea

Show current dots moving through resistors while node currents and loop voltage drops light up one by one.

02

Nodal Analysis

Nodal analysis solves a circuit by focusing on node voltages instead of branch currents.

Concept Breakdown

  • A node is a connection point shared by circuit branches.
  • One node is chosen as ground, so every other voltage is measured from it.
  • Current through each connected branch is written using the node voltage.
  • KCL turns those branch currents into equations.

Formula

I = (Vnode - Vother) / R

  • Vnode is the voltage at the node you are solving.
  • Vother is the voltage at the other end of the branch.
  • R is the resistance in that branch.

Step-by-Step Method

  1. 1Choose the ground node.
  2. 2Name the unknown node voltages.
  3. 3Write KCL at each important node.
  4. 4Convert branch currents using voltage difference divided by resistance.
  5. 5Solve the node-voltage equations.
  6. 6Use the voltages to find required currents and power.

Key Idea

Nodal analysis is best when node voltages are easier to find than loop currents.

Animation Idea

Highlight the ground node first, then show currents leaving each node as equations appear beside them.

03

Mesh Analysis

Mesh analysis solves a circuit by assigning a current to each loop and tracking voltage drops.

Concept Breakdown

  • A mesh is a loop that does not contain another loop inside it.
  • Each mesh gets its own assumed current direction.
  • Shared resistors carry the difference between two mesh currents.
  • KVL around each mesh creates the equations.

Formula

Vdrop = R(Imesh1 - Imesh2)

  • R is the shared resistance.
  • Imesh1 is the current of the loop you are writing.
  • Imesh2 is the neighboring loop current through the same resistor.

Step-by-Step Method

  1. 1Identify the independent meshes.
  2. 2Assign clockwise or anticlockwise mesh currents.
  3. 3Write KVL around each mesh.
  4. 4Handle shared resistors using current differences.
  5. 5Solve the mesh-current equations.
  6. 6Use mesh currents to find branch currents and voltages.

Key Idea

Mesh analysis is best when loop currents make the circuit easier to describe.

Animation Idea

Draw glowing circular arrows around each loop, then highlight shared resistors where currents oppose or assist.

04

Source Transformation

Source transformation changes the shape of a source branch while keeping the outside behavior the same.

Concept Breakdown

  • A voltage source with a series resistor can become a current source with a parallel resistor.
  • A current source with a parallel resistor can become a voltage source with a series resistor.
  • The load connected to the terminals sees the same voltage-current behavior.
  • This is useful when the new shape reveals simpler series or parallel paths.

Formula

V = IR

  • V is the equivalent voltage source value.
  • I is the equivalent current source value.
  • R is the same resistor used in both forms.

Step-by-Step Method

  1. 1Find a source with its matching resistor.
  2. 2Check whether it is voltage-series or current-parallel form.
  3. 3Use V = IR to convert source value.
  4. 4Keep the resistor value the same.
  5. 5Redraw the circuit and simplify the new connections.

Key Idea

Source transformation changes circuit form without changing terminal behavior.

Animation Idea

Show a battery and series resistor morphing into a current source and parallel resistor.

05

Thevenin and Norton Methods

Thevenin and Norton methods replace a large network with a small equivalent seen by the load.

Concept Breakdown

  • Thevenin uses one voltage source with one series resistor.
  • Norton uses one current source with one parallel resistor.
  • Both describe the same two-terminal behavior.
  • They are useful when the load changes or when a circuit is too large to solve repeatedly.

Formula

Vth = In Rth

  • Vth is the Thevenin voltage.
  • In is the Norton current.
  • Rth is the same equivalent resistance used in both forms.

Step-by-Step Method

  1. 1Remove the load from the output terminals.
  2. 2Find the open-circuit voltage for Thevenin.
  3. 3Find the short-circuit current for Norton.
  4. 4Find the equivalent resistance seen from the terminals.
  5. 5Draw the simpler equivalent circuit.
  6. 6Reconnect the load and solve quickly.

Key Idea

A complex network can be replaced by a simple equivalent at the load terminals.

Animation Idea

Collapse a complex network into Thevenin form, then flip it into Norton form while the load stays connected.

06

Superposition Method

Superposition handles multiple independent sources by studying one source at a time.

Concept Breakdown

  • Only one independent source is kept active during each pass.
  • Other independent voltage sources become short circuits.
  • Other independent current sources become open circuits.
  • Each partial voltage or current is added to get the final result.

Formula

final response = response1 + response2 + ...

  • Response means the voltage or current you are finding.
  • Each response comes from one active source.
  • Signs matter because directions and polarities matter.

Step-by-Step Method

  1. 1Choose the voltage or current to find.
  2. 2Keep one independent source active.
  3. 3Turn off all other independent sources.
  4. 4Solve the circuit for that single source.
  5. 5Repeat for every independent source.
  6. 6Add the partial results with correct sign or direction.

Key Idea

Superposition breaks a multi-source circuit into smaller single-source circuits.

Animation Idea

Fade all sources except one, show its current path, then combine colored paths into the final response.

One DC Analysis Flow

DC analysis is not about memorizing one method. It is about reading the circuit and choosing the cleanest path to the answer.

  1. Step 1

    Read the circuit and mark nodes, loops, sources, and resistors.

  2. Step 2

    Decide whether the circuit is easier by nodes, meshes, or direct laws.

  3. Step 3

    Simplify first if source transformation or equivalents reduce the circuit.

  4. Step 4

    Write equations using Ohm's Law, KCL, or KVL.

  5. Step 5

    Solve for unknown voltages and currents.

  6. Step 6

    Check power direction and signs to confirm the result makes physical sense.

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