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### Goal: To understand uses for induction

Objectives:

1) To learn how to use Lenz’s Law to determine the direction of an induced current or magnetic field

2) To learn how to use Transformers

3) To learn about Inductors

4) To be able to calculate the Energy stored inside an inductor

5) To learn about LR circuits

Lenz’s Law

- V = - N Δ Φ / Δt
- This is for a coil.
- If the magnetic field decreases then we will produce a positive EMF.
- An increase in the magnetic field likewise will produce a negative EMF.
- The magnetic field induced from the EMF produces a magnetic flux which counteracts the change in magnetic flux!
- So, when the magnetic field increases (in the + direction) you induce a negative magnetic flux from the current which gives a clockwise current.
- A decreasing magnetic field (in the + direction) induces a counter-clockwise current (which produces a positive magnetic flux).
- Note: if you change a negative magnetic field then you have to notice that an increased magnitude is really decreasing the magnetic field.
- Bottom line is find the current which produces a magnetic field which offsets the change in the magnetic field.

Example:

- From HW 6:
- A coil rests upright on your desk.
- A magnetic field which is at a 90 degree angle to your desk causes a clockwise current in the coil.
- What must be true about the direction and magnitudes of the magnetic field?
- 1) upwards from desk and increasing with time
- 2) upwards from desk and constant with time
- 3) downwards toward desk and increasing in magnitude with time
- 4) downwards from the desk and constant with time

Example:

- From HW 6:
- A coil rests upright on your desk.
- A magnetic field which is at a 90 degree angle to your desk causes a clockwise current in the coil.
- What must be true about the direction and magnitudes of the magnetic field?
- 1) upwards from desk and increasing with time
- Constant magnetic field will not induce current!
- A clockwise current induces a negative magnetic flux.
- Since this is opposite to the change (to try to counteract) that means the field must be increasing.
- The downwards one was only increasing in magnitude… A larger negative value is actually lower…

Yesterday we saw:

- V = - N Δ Φ / Δt
- This is for a coil.
- Imagine you had 2 coils.
- The first coil would affect the 2nd coil!
- So, V1 = - N1 Δ Φ / Δt
- And: V2 = - N2 Δ Φ / Δt
- Since Δ Φ / Δt is the same for both coils then you get that:
- V1/V2 = N1 / N2
- This is a transformer!

Transformers

- Transformers transform 1 voltage to another.
- For example high voltage power lines carry large amounts of energy long distances.
- They do this to save on losses.
- Then, they transform that from 100k volts to the 120 volts you use in your home using a series of transformers.

Current in transformer

- You cannot gain energy – so the energy you get in one is the same as the other.
- Therefore the powers are also the same!
- So, P1 = P2
- Since P = IV therefore
- I1V1 = I2V2 (or I1/I2 = V2/V1)
- Since V2/V1 = N2/N1, therefore, I1/I2 = N2 / N1
- When you shrink the voltage you increase the current and visa versa.

Sample

- A 120k voltage line carries 0.1 A of current.
- This line is passed through a transformer.
- The high voltage end has 3000 loops and the low end has 3 loops. After the 3 loops is a simple light bulb.
- A) What is the power that is passed through the receiver to the light bulb?
- B) what is the current which the light bulb receives?
- C) What is the voltage across the 3 loop transistor?

Transformer types

- There are 2 types of transformers:
- Step up transformers – these step up the voltage (and decrease the current).
- These start with a small # of loops and the other end has a large # of loops.
- If you reverse the step up transformer then you have a step down transformer.
- These start with a large # of loops and end up with a small # of loops – and decrease the voltage while increasing current.

Inductors

- Inductors are the magnetic equivalent to the electric fields capacitor.
- Just like capacitors store electric energy Inductors store magnetic energy.
- Capacitance was how effectively you could store charge, and Inductance is how well you can store a magnetic field.
- So, inductance (denoted as L) is:
- L = N Φ/ I (l here is length)

Equations

- An inductor with length l and having N turns has inductance of:
- L = μ0 N2πr2 / l
- And the emf in a coil is just
- V = - N Δ Φ / Δt = - L Δ i / Δt
- And the power going through the inductor is:
- P = V i where i is the current at some point in time and I is the final current.
- The average power is:
- Pav = ½ Vi

Energy in an inductor

- U = ½ Li2
- And in a circuit inductors add up the same way as resistors.

LR circuits

- We saw RC circuits now we have LR circuits.
- Again we have a time constant.
- However, this time τ = L/R
- Everything else is the same as for RC circuits.
- No examples here, we are out of time!

Conclusion

- We saw with Lenz’s law that a change in magnetic field will induce a current such that the induced current will induce a magnetic flux to counteract the change in magnetic field.
- We learned about transformers and saw that while power is constant that we drop/raise voltage and raise/drop current depending on whether we have less/more loops on the end we are transferring to.
- We learned about inductors.
- We saw the energy stored in an inductor and inductors in LR circuits.

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