190 likes | 336 Views
RL Circuits. Physics 102 Professor Lee Carkner Lecture 21. PAL #21 Generator. To produce 12 amps in a 15 ohm wire you need an emf of e = IR = (12)(15) = 180 V Set 180 V equal to the max emf e = NBA w w = e /NBA = 180/(1)(2)(1) = 90 rad/s If w = 90 rad/s, we can find f = w /2 p
E N D
RL Circuits Physics 102 Professor Lee Carkner Lecture 21
PAL #21 Generator • To produce 12 amps in a 15 ohm wire you need an emf of e = IR = (12)(15) = 180 V • Set 180 V equal to the max emf • e = NBAw • w = e/NBA = 180/(1)(2)(1) = 90 rad/s • If w = 90 rad/s, we can find f = w/2p • 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: e = -N(DF/Dt) • If we put the coil properties into the variable “L” we get: e = -L(DI/Dt) • where the constant of proportionality L is the inductance • The unit of inductance is the Henry, • H (V s/A)
Inductance e = L(DI/Dt) = N(DF/Dt) L = N(DF/DI) L = m0n2Al • 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 mB = (B2/2m0) • 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
Transformer • The emf then only depends on the number of turns in each e = N(DF/Dt) 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? • Increasing the strength of the magnetic field • Increasing the velocity of the rod • Increasing the length of the rod • Increasing the thickness of the rod • Nothing can change the emf of the rod
Household electrical current has a frequency of 60 Hz. What is its angular frequency? • 9.5 rad/s • 60 rad/s • 188 rad/s • 377 rad/s • 600 rad/s
If the frequency of a generator is increased, • The maximum emf goes up and the current changes direction more rapidly • The maximum emf goes up and the current changes direction less rapidly • The maximum emf goes down and the current changes direction more rapidly • The maximum emf goes down and the current changes direction less rapidly • The maximum emf does not change