Hey, guys. So we saw how in the last couple of videos, a coil of wire with a change in current can actually induce an EMF on itself. That was self inductance. But sometimes you need to know how these coils of wire behave in circuits. So we're going to go ahead and take a look at that in this video. Alright. So basically, if you place a coil of wire inside a circuit, it's known as an inductor. It's kind of like how we talked about capacitance and then we talked about capacitors and circuits. Then we talked about resistance and then resistors in circuits. Here we talked about inductance. Now, we're going to talk about inductors and how they behave in circuits. So, there are 2 common symbols that you're going to see in your classroom, in your textbooks. You're going to see this little bumpy guy right here, and then you're going to see this little loopy one. I actually kind of prefer the loopy one just because I can't draw this that well. So for the rest of this video, I'm going to use these loops right here in the context of inductors. Alright? So just be aware that you can see both of those symbols there. It's the same thing. Alright. So because these inductors are circuit elements and we use them in circuits, we need to be able to use Kirchhoff's rules as we go around them in a circuit. Right? So we need to be able to use the loop rule and figure out what the voltages are. Now the first things first, we have to remember that inductors only do something if the current is changing. We saw that for a coil of wire, the self inductance, given by this little letter L is negative L times delta I over delta t. So they relate the current changing to the self-induced EMF. So what happens is if we have this diagram here and the current is constant, then that means that the change in the current over change in time is equal to 0, and there's going to be no EMF. So this inductor right here isn't doing anything because there is no change in the current. So it's only that when you have either an increasing or decreasing current in a circuit, you're going to get some kind of EMF. So we have EMF here, and we have EMF here. But what happens is that it's not just enough to know the magnitude of the EMF, we also need to know the direction and whether it's positive or negative in order to use Kirchhoff's rules. So we've got a battery right here and we've got a current that's going to go in this direction like this. So this is going to be our direction. And whenever we do Kirchhoff's rules, we have to basically pick up points like this, and then we have to go around in a loop and then add up all the voltages. The problem is that I don't know whether the voltage across this inductor is going to be positive or negative, and the same thing goes over here for this diagram as well. So, in order to do that, I need to use Lenz's law to figure out what the direction is of the induced EMF of the inductor. So let's take a look at this. Right? You have a coil of wire and it's going to generate a magnetic field in this direction. And what happens is that magnetic field is proportional to the current. So if the current is increasing, then the strength of the magnetic field is getting stronger. And so what happens is Lenz's law, which gives us which is given by this minus sign in this equation right here, tells us that the induced EMF is going to be the opposite of whatever the system is doing. So that means if I were to try to figure out what the induced EMF is on the circuit, it's going to be the opposite of whatever it wants to do. So if it's going in this direction and it's increasing, the induced EMF is going to go this way. Now let's take a look at this example, where the only thing that's different is that the current now is decreasing. So it still goes in this direction, and our loop is still going to be in this direction. But now what happens is that our EMF induced, if the current is decreasing, it actually wants to reinforce the weakening magnetic field. So the induced EMF is actually going to point along that direction. Okay. So it's not about where the direction of the current is. It's about where the current is pointing, and whether it's getting stronger or weaker. Now the thing is if the direction of your induced EMF, and this is the most important part here. If the direction of your induced EMF points along our Kirchhoff loop, then the voltage it picks up is actually going to be positive. So what happens here is if our loop is in this direction, so this is our loop, and my induced EMF points in this direction like this, then it's going to be positive. If it points in this direction, then that induced EMF is going to be negative for our Kirchhoff's loop. And the same thing goes for the opposite direction. If our loop points in this direction and we have an EMF that points in that direction, then it's going to be positive. And if it points in this direction, then it's going to be negative. Alright? So when we use our Kirchhoff's loops, these are the rules that we have to follow. Alright. So let's go ahead and take a look at an example here. We've got Kirchhoff's loop rule for the following circuit, and we're going to assume that the voltages of the battery is increasing. So let's see. We've got a battery like this, so I have a voltage from the battery, then we have a voltage from the inductor, that's going to be v l, and then we have a resistor right here, so it's also going to have a voltage. So what I'm going to do is I'm just going to go ahead and pick a direction for my loop. So I'm just going to go ahead and choose this direction. And let's see. The battery actually has the positive terminal that goes to the left. So that means that I know the current is going to be in this direction. So that's I. So it means the current is this, and the current is this. And I also know that that current is increasing. So now what I want to do is figure out

Table of contents

- 0. Math Review31m
- 1. Intro to Physics Units1h 23m
- 2. 1D Motion / Kinematics3h 56m
- Vectors, Scalars, & Displacement13m
- Average Velocity32m
- Intro to Acceleration7m
- Position-Time Graphs & Velocity26m
- Conceptual Problems with Position-Time Graphs22m
- Velocity-Time Graphs & Acceleration5m
- Calculating Displacement from Velocity-Time Graphs15m
- Conceptual Problems with Velocity-Time Graphs10m
- Calculating Change in Velocity from Acceleration-Time Graphs10m
- Graphing Position, Velocity, and Acceleration Graphs11m
- Kinematics Equations37m
- Vertical Motion and Free Fall19m
- Catch/Overtake Problems23m

- 3. Vectors2h 43m
- Review of Vectors vs. Scalars1m
- Introduction to Vectors7m
- Adding Vectors Graphically22m
- Vector Composition & Decomposition11m
- Adding Vectors by Components13m
- Trig Review24m
- Unit Vectors15m
- Introduction to Dot Product (Scalar Product)12m
- Calculating Dot Product Using Components12m
- Intro to Cross Product (Vector Product)23m
- Calculating Cross Product Using Components17m

- 4. 2D Kinematics1h 42m
- 5. Projectile Motion3h 6m
- 6. Intro to Forces (Dynamics)3h 22m
- 7. Friction, Inclines, Systems2h 44m
- 8. Centripetal Forces & Gravitation7h 26m
- Uniform Circular Motion7m
- Period and Frequency in Uniform Circular Motion20m
- Centripetal Forces15m
- Vertical Centripetal Forces10m
- Flat Curves9m
- Banked Curves10m
- Newton's Law of Gravity30m
- Gravitational Forces in 2D25m
- Acceleration Due to Gravity13m
- Satellite Motion: Intro5m
- Satellite Motion: Speed & Period35m
- Geosynchronous Orbits15m
- Overview of Kepler's Laws5m
- Kepler's First Law11m
- Kepler's Third Law16m
- Kepler's Third Law for Elliptical Orbits15m
- Gravitational Potential Energy21m
- Gravitational Potential Energy for Systems of Masses17m
- Escape Velocity21m
- Energy of Circular Orbits23m
- Energy of Elliptical Orbits36m
- Black Holes16m
- Gravitational Force Inside the Earth13m
- Mass Distribution with Calculus45m

- 9. Work & Energy1h 59m
- 10. Conservation of Energy2h 51m
- Intro to Energy Types3m
- Gravitational Potential Energy10m
- Intro to Conservation of Energy29m
- Energy with Non-Conservative Forces20m
- Springs & Elastic Potential Energy19m
- Solving Projectile Motion Using Energy13m
- Motion Along Curved Paths4m
- Rollercoaster Problems13m
- Pendulum Problems13m
- Energy in Connected Objects (Systems)24m
- Force & Potential Energy18m

- 11. Momentum & Impulse3h 40m
- Intro to Momentum11m
- Intro to Impulse14m
- Impulse with Variable Forces12m
- Intro to Conservation of Momentum17m
- Push-Away Problems19m
- Types of Collisions4m
- Completely Inelastic Collisions28m
- Adding Mass to a Moving System8m
- Collisions & Motion (Momentum & Energy)26m
- Ballistic Pendulum14m
- Collisions with Springs13m
- Elastic Collisions24m
- How to Identify the Type of Collision9m
- Intro to Center of Mass15m

- 12. Rotational Kinematics2h 59m
- 13. Rotational Inertia & Energy7h 4m
- More Conservation of Energy Problems54m
- Conservation of Energy in Rolling Motion45m
- Parallel Axis Theorem13m
- Intro to Moment of Inertia28m
- Moment of Inertia via Integration18m
- Moment of Inertia of Systems23m
- Moment of Inertia & Mass Distribution10m
- Intro to Rotational Kinetic Energy16m
- Energy of Rolling Motion18m
- Types of Motion & Energy24m
- Conservation of Energy with Rotation35m
- Torque with Kinematic Equations56m
- Rotational Dynamics with Two Motions50m
- Rotational Dynamics of Rolling Motion27m

- 14. Torque & Rotational Dynamics2h 5m
- 15. Rotational Equilibrium3h 39m
- 16. Angular Momentum3h 6m
- Opening/Closing Arms on Rotating Stool18m
- Conservation of Angular Momentum46m
- Angular Momentum & Newton's Second Law10m
- Intro to Angular Collisions15m
- Jumping Into/Out of Moving Disc23m
- Spinning on String of Variable Length20m
- Angular Collisions with Linear Motion8m
- Intro to Angular Momentum15m
- Angular Momentum of a Point Mass21m
- Angular Momentum of Objects in Linear Motion7m

- 17. Periodic Motion2h 9m
- 18. Waves & Sound3h 40m
- Intro to Waves11m
- Velocity of Transverse Waves21m
- Velocity of Longitudinal Waves11m
- Wave Functions31m
- Phase Constant14m
- Average Power of Waves on Strings9m
- Wave Intensity19m
- Sound Intensity13m
- Wave Interference8m
- Superposition of Wave Functions3m
- Standing Waves30m
- Standing Wave Functions14m
- Standing Sound Waves12m
- Beats8m
- The Doppler Effect7m

- 19. Fluid Mechanics2h 27m
- 20. Heat and Temperature3h 7m
- Temperature16m
- Linear Thermal Expansion14m
- Volume Thermal Expansion14m
- Moles and Avogadro's Number14m
- Specific Heat & Temperature Changes12m
- Latent Heat & Phase Changes16m
- Intro to Calorimetry21m
- Calorimetry with Temperature and Phase Changes15m
- Advanced Calorimetry: Equilibrium Temperature with Phase Changes9m
- Phase Diagrams, Triple Points and Critical Points6m
- Heat Transfer44m

- 21. Kinetic Theory of Ideal Gases1h 50m
- 22. The First Law of Thermodynamics1h 26m
- 23. The Second Law of Thermodynamics3h 11m
- 24. Electric Force & Field; Gauss' Law3h 42m
- 25. Electric Potential1h 51m
- 26. Capacitors & Dielectrics2h 2m
- 27. Resistors & DC Circuits2h 7m
- 28. Magnetic Fields and Forces2h 23m
- 29. Sources of Magnetic Field2h 31m
- Magnetic Field Produced by Moving Charges10m
- Magnetic Field Produced by Straight Currents27m
- Magnetic Force Between Parallel Currents12m
- Magnetic Force Between Two Moving Charges9m
- Magnetic Field Produced by Loops and Solenoids43m
- Toroidal Solenoids aka Toroids12m
- Biot-Savart Law (Calculus)18m
- Ampere's Law (Calculus)17m

- 30. Induction and Inductance3h 37m
- 31. Alternating Current2h 37m
- Alternating Voltages and Currents18m
- RMS Current and Voltage9m
- Phasors20m
- Resistors in AC Circuits9m
- Phasors for Resistors7m
- Capacitors in AC Circuits16m
- Phasors for Capacitors8m
- Inductors in AC Circuits13m
- Phasors for Inductors7m
- Impedance in AC Circuits18m
- Series LRC Circuits11m
- Resonance in Series LRC Circuits10m
- Power in AC Circuits5m

- 32. Electromagnetic Waves2h 14m
- 33. Geometric Optics2h 57m
- 34. Wave Optics1h 15m
- 35. Special Relativity2h 10m

30. Induction and Inductance

Inductors

30. Induction and Inductance

# Inductors - Online Tutor, Practice Problems & Exam Prep

Created using AI

Inductors, represented by symbols like a bumpy line or loops, are crucial in circuits as they induce electromotive force (emf) when current changes. According to Lenz's law, the induced emf opposes the change in current, affecting its direction and sign in Kirchhoff's loop rule. For a circuit with an increasing current, the induced emf is negative, while for a decreasing current, it reinforces the magnetic field. The relationship is expressed as $\epsilon =-L\frac{\mathrm{\Delta I}}{\mathrm{\Delta t}}$, essential for analyzing circuit behavior.

concept

### Inductors in Circuits

Video duration:

7mPlay a video:

#### Video transcript

## Do you want more practice?

More sets### Your Physics tutor

Additional resources for Inductors

PRACTICE PROBLEMS AND ACTIVITIES (6)

- A toroidal solenoid has mean radius 12.0 cm and crosssectional area 0.600 cm^2. (a) How many turns does the so...
- The inductor shown in Fig. E30.11 has inductance 0.260 H and carries a current in the direction shown. The cur...
- When the current in a toroidal solenoid is changing at a rate of 0.0260 A/s, the magnitude of the induced emf ...
- How much energy is stored in a 3.0-cm-diameter, 12-cm-long solenoid that has 200 turns of wire and carries a c...
- Assuming the Earth’s magnetic field averages about 0.50 x 10⁻⁴ T near the surface of the Earth, estimate the t...
- (II) A long straight wire of radius r carries current I uniformly distributed across its cross-sectional area....