Network Analysis

Circuit Laws

Circuit laws help us predict how a circuit settles after a source is connected. Ohm's Law explains flow through an element. KCL explains what happens at a junction. KVL explains how energy balances around a closed path.

Ohm's Law

Ohm's Law connects the push, the flow, and the opposition in a circuit.

Visual Understanding

Voltage acts like the push that tries to move charge through the path.
Current is the actual movement of charge through the component.
Resistance makes that movement harder, so the current becomes smaller.
If voltage increases and resistance stays the same, current increases.
If resistance increases and voltage stays the same, current decreases.

Formula

V = IR

V is the voltage across the element. It shows how much electrical push is available.
I is the current through the element. It shows how much charge is moving.
R is the resistance. It shows how strongly the element slows current.

Simple Example

If the same resistor is connected to a stronger battery, current moves faster. If a bigger resistor is used with the same battery, current slows down.

Key Idea

Voltage pushes, resistance limits, and current is the result.

Animation Idea

Show current dots speeding up when voltage increases and slowing down when the resistor becomes larger.

Kirchhoff's Current Law (KCL)

KCL helps us understand what happens when current reaches a junction.

Visual Understanding

A junction is a meeting point where wires or branches connect.
Current may split into different branches or combine from different branches.
The node does not store charge like a tank.
So the current arriving at the node must be matched by current leaving it.
This is why node analysis works: every junction has a current balance.

Formula

current entering = current leaving

Entering current means current flowing into the node.
Leaving current means current flowing out through connected branches.
The balance means charge is not piling up at the junction.

Simple Example

If 6 A enters a junction and one branch takes 2 A, the remaining branches together must carry 4 A away.

Key Idea

At a junction, current splits or combines, but charge does not disappear.

Animation Idea

Show moving current dots reaching a node and splitting into two or three branch paths.

Kirchhoff's Voltage Law (KVL)

KVL helps us track energy as charge moves around a closed loop.

Visual Understanding

A voltage source gives energy to the charge.
Components use that energy as the charge moves through them.
When we return to the starting point of the loop, the energy balance must be complete.
The voltage gained from sources is used as voltage drops across components.
This is why loop equations work: the loop cannot create extra energy by itself.

Formula

sum of voltages around a loop = 0

Voltage rise means energy is added, usually by a source.
Voltage drop means energy is used by a component.
The total becomes zero because every gain is balanced by drops in a closed loop.

Simple Example

In a simple battery-resistor loop, the battery may add 12 V. The resistor then drops 12 V, so the loop balances.

Key Idea

Around a closed loop, energy gained equals energy used.

Animation Idea

Show a bright energy bar rising at the battery and fading step by step across each component.

How The Laws Work Together

In a real circuit, these laws do not act separately. Voltage starts the action. Resistance shapes the current. Nodes split and combine current. Loops balance voltage rises and drops. A correct circuit solution must satisfy all three at the same time.

Step 1

Voltage Applied

A source creates electrical push across the circuit.

Step 2

Current Starts

Ohm's Law decides how much current flows through each resistive path.

Step 3

Current Splits

At junctions, KCL keeps incoming and outgoing current balanced.

Step 4

Voltage Drops

Across components, voltage is used as electrical energy is converted or stored.

Step 5

Loop Balances

KVL makes sure the total voltage rise and total voltage drop match.

Step 6

Stable Operation

The circuit settles into values that satisfy Ohm's Law, KCL, and KVL together.

Circuit Elements Next Network Theorems