The Loop Rule

Part of the Electricity and Magnetism section of Coddy's Physics journey. Lesson 31 of 51.

Around any closed loop the voltage changes add up to zero:

$\Sigma \varepsilon = \Sigma IR$

Through a battery from − to +: gain ε. Through a resistor along your current: lose IR.

A loop with two batteries

Challenge

One loop: a $12\ \mathrm{V}$ battery and a $4\ \mathrm{V}$ battery facing the opposite way, with a $3\ \mathrm{\Omega }$ and a $1\ \mathrm{\Omega }$ resistor. What current $I$ flows? Give it a direction first.

Try it yourself

Solve for $I$

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Electricity and Magnetism

1Electric Charge and Force

Electric Charge Coulomb's Law Several Charges Recap - Charges in a Line

4Charged Conductors

The Charged Sphere Connecting Spheres Recap - Beam Between Plates

7Real Batteries

Internal Resistance The Variable Resistor Ammeters and Voltmeters Recap - Flashlight

10Magnetic Fields

Magnets and Magnetic Fields Field of a Wire Loops and Solenoids Recap - Electromagnet

2The Electric Field

The Electric Field Field of Several Charges The Uniform Field A Charge in a Uniform Field Recap - Stopping a Proton

5Capacitors

The Capacitor Combining Capacitors Changing a Capacitor Recap - Camera Flash

8Kirchhoff's Laws

The Junction RuleThe Loop RuleSolving Two Loops Recap - Charging a Battery

11Magnetic Forces

Force on a Moving Charge Circles in a Field Force on a Wire Two Parallel Wires Recap - Current Balance

3Energy and Potential

Electric Potential Energy Electric Potential Field and Potential Recap - Accelerating Ions

6Current and Resistance

Current and Voltage Resistance and Ohm's Law Series and Parallel Electric Power Recap - Fairy Lights

9Capacitors in Circuits

A Capacitor in a Circuit Charging a Capacitor Discharging a Capacitor Recap - Defibrillator

12Induction

A Rod Moving in a Field Magnetic Flux Faraday's Law Lenz's Law Recap - Generator