RL Circuits

Physics 102Professor Lee

CarknerLecture 22

PAL #21 Generator

Set 180 V equal to the max emf = = /NBA = 180/(1)(2)(1) = 90 rad/s If = 90 rad/s, we can find f = /2 f =

Induction and Circuits

The changing magnetic field can then induce a current

This means,

Note that induction only applies in circuits where the current changes often this means a switch is closed or opened

Self Inductance

When the switch is closed, current flows through the loop, inducing a B field through the loop

Called self inductance

Back emf

Works like a battery that is put in “backwards” Direction of emf depends on how current

changes

Current increases, emf in reverse direction Current decreases, emf in same direction

Inductance and Increasing

Current

Effect of Back emf

Finding emf

emf depends on Faraday’s Law:

But the magnetic flux depends on the changing current and the properties of the coil

= -L(I/t)

where the constant of proportionality L is the inductance

Inductance The unit of inductance is the henry,

The inductance of a circuit element (like a

solenoid) depends on the current and the flux flowing through it

L = N(/I)

Inductance is a property of the circuit element Like resistance

Solenoid Inductance To find L, we need a relationship between and I

What is (/I)?

= BA cos or = BA

B = 0(N/l)I or I = Bl/(0N) L = N(/I) = N/I = NBA0N/Bl = 0N2A/l

L = 0n2Al

Inductors

In a circuit any element with a high inductance is represented by an inductor

We will assume that the rest of the circuit has negligible inductance

Symbol is a spiral:

Today’s PAL

A solenoid that is 5 cm long and 1 cm in diameter is placed in a circuit. If 0.1 V of emf is induced by increasing the current from 0 to 3 A in 0.5 seconds, how many turns does the solenoid have?

RL Circuits

As current tries to flow, it is resisted by the inductor

Time depends on R and L

Current can’t get to max value or 0 instantly

A RL Circuit

Time Constant

The characteristic time is given as:

Larger inductance means longer delay

I = (/R)[1 - e(-t/)]

Note the similarities to a RC circuit

Current Rise with Time

Energy in an Inductor

This work can be thought of as energy stored in the inductor

E = (1/2) L I2

E and I are the values for the circuit after a “long time”

Magnetic Energy

Where is this energy stored?

Magnetic fields, like electric fields both represent energy

B = (B2/20) This is how much energy per cubic meter is

stored in a magnetic field B

Transforming Voltage

It is important to provide an electrical device with the right voltage

We often only have a single source of emf

We can use the fact that a voltage

through a solenoid will induce a magnetic field, which can induce an emf in another solenoid

Basic Transformer

Transformer

The emf then only depends on the number of turns in each

The ratio of emf’s is then just equal to the ratio of turns

Vp/Vs = Np/Ns

Device is called a transformer If Np > Ns, voltage decreases If Ns > Np voltage increases

Transformers and Current

Energy is conserved in a transformer so: Vp/Vs = Is/Ip

Note that the flux must be

changing, and thus the current must be changing

Transformer Applications

Generators usually operate at ~10,000 volts

Since P = I2R a small current is best for

transmission wires Power pole transformers step the voltage

down for household use to 120 or 240 V

Next Time

Read 21.12 Homework, Ch 21, P 36, 43, 47, 53