Solving Two Loops

Part of the Electricity and Magnetism section of Coddy's Physics journey. Lesson 32 of 51.

Three unknown currents need three equations: one junction rule and two loop rules.

Two loops

Give each current a direction, write the rules with those directions, and solve them together. A negative current flows the other way.

Challenge

In the circuit, ε₁ = ε₂ = $12\ \mathrm{V}$ , R₁ = $2\ \mathrm{\Omega }$ , and R₂ = R₃ = $4\ \mathrm{\Omega }$ . What current $\relax I_{3}$ flows through R₃? Give every current a direction first.

Try it yourself

Solve for $I_{3}$

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 Rule The Loop RuleSolving Two LoopsRecap - 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