RL Circuits

Physics 102Professor Lee

CarknerLecture 21

PAL #21 Generator

To produce 12 amps in a 15 ohm wire you need an emf of = IR = (12)(15) = 180 V

Set 180 V equal to the max emf = NBA = /NBA = 180/(1)(2)(1) = 90 rad/s If = 90 rad/s, we can find f = /2 f = 14.3 Hz or 14.3 cycles per second

Induction and Circuits

The changing magnetic field can then induce its own current that will oppose the initial changes

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

The emf induced opposes the direction of the current change

Called the back emf Current decreases, emf in same direction

Finding emf The back emf depends on Faraday’s Law:

= -N(/t)

If we put the coil properties into the variable “L” we get:

= -L(I/t)

where the constant of proportionality L is the inductance

The unit of inductance is the Henry, H (V s/A)

Inductance

= L(I/t) = N(/t)L = N(/I)

L = 0n2Al n= A = cross sectional area l = length

Inductors

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

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

Symbol is a spiral:

Magnetic Energy

A battery must do work to overcome the back emf of a circuit with inductance Magnetic fields, like electric fields represent energy

Energy in an inductor is:E = (1/2) L I2

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

a magnetic field B

Transforming Voltage

We often only have a single source of emf e.g. household current at 120 V

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

= N(/t)

Vp/Vs = Np/Ns Where p and s are the primary and secondary solenoids

If Np > Ns, voltage decreases (is stepped down) If Ns > Np voltage increases (is stepped up)

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 Transformers only work for AC current

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

A metal rod moves horizontally in a uniform vertical magnetic field. Which of the following changes would not increase the emf induced across the rod?

A) Increasing the strength of the magnetic field

B) Increasing the velocity of the rodC) Increasing the length of the rodD) Increasing the thickness of the rodE) Nothing can change the emf of the

rod

Household electrical current has a frequency of 60 Hz. What is its angular frequency?

A) 9.5 rad/sB) 60 rad/sC) 188 rad/sD) 377 rad/sE) 600 rad/s

If the frequency of a generator is increased,

A) The maximum emf goes up and the current changes direction more rapidly

B) The maximum emf goes up and the current changes direction less rapidly

C) The maximum emf goes down and the current changes direction more rapidly

D) The maximum emf goes down and the current changes direction less rapidly

E) The maximum emf does not change