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Kirchhoff's Laws

Introduction

Kirchhoff's Laws are two fundamental principles that govern how current and voltage behave in circuits. Named after German physicist Gustav Kirchhoff, these laws are essential for analyzing complex circuits.

Our circuit simulator uses these laws to calculate realistic behavior in your designs!

Kirchhoff's Current Law (KCL)

The Law:

The sum of all currents entering a node equals the sum of all currents leaving that node.

Σ I_in = Σ I_out

In simple terms: Current can't just disappear or appear out of nowhere. Whatever flows into a junction must flow out of it.

Example:

If 100mA flows into a junction and splits into two branches, maybe 60mA goes down one path and 40mA down the other. The total out (60mA + 40mA) equals the total in (100mA).

Why it matters: KCL helps us analyze parallel circuits and understand how current divides among multiple paths.
Kirchhoff's Voltage Law (KVL)

The Law:

The sum of all voltage rises and drops around any closed loop in a circuit equals zero.

Σ V_loop = 0

In simple terms: The voltage supplied by the power source equals the sum of all voltage drops across components in the loop.

Example:

A 9V battery powers two resistors in series:

  • Resistor 1 drops 5V
  • Resistor 2 drops 4V
  • Total: 5V + 4V = 9V ✓

The voltage drops (9V) equal the voltage rise from the battery (9V)!

Why it matters: KVL is crucial for series circuits. It ensures energy conservation - the energy supplied equals the energy used.
Practical Application: LED Circuit Analysis

Let's analyze a circuit with a 5V battery, a 220Ω resistor, and a red LED in series:

Step 1: Apply KVL around the loop

V_battery = V_resistor + V_LED

5V = V_resistor + 1.8V

V_resistor = 3.2V

Step 2: Use Ohm's Law to find current

I = V_resistor / R = 3.2V / 220Ω = 14.5mA

Step 3: Verify with KCL

Since this is a series circuit, the same 14.5mA flows through the battery, resistor, and LED. KCL is satisfied at every junction!

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