a motor converts ______________energy into __________energy. a motor converts ______________energy...
TRANSCRIPT
Induced Voltage:Three Cases
• The B Field can change :
V= NA(DB /Dt )
• The area can change (motional emf):
V= BLv
• The angle can change (generator):
V = wNBA sinwt
The B Field can change :
V= NA(DB /Dt )
Example: A magnet is moved into a coil with 100 turns and an area .10m2. The field in the loop changes from zero to 2T in .1 seconds. 1. What is the induced voltage? V = NA(DB /Dt ) = (100)(.1)( 2/.1) = 200Volts2. If the coil has a resistance of 100 Ohms, what’s the current in the coil?
I = V/R = 200/100= 2 Amps
The area can change: V= Blv
Example: A metal bar moves to the right with a velocity of 10m/s through a magnetic field of 3T. The loop height, L, is .5m.
1. What is the induced voltage?
2. If the circuit has a resistance of 2 Ohms, what’s the current in the circuit?
V = BLv = (3)(.5)( 10) = 15Volts
I = V/R = 15/2= 7.5 Amps
The angle can change: V= wNBA sinwt
Example: A generator turns at 100rad/sec. It has 500 turns, and a magnetic field of .5T. The loop area is.01 m2. What is the maximum voltage?
This is used for the generator. The maximum voltage is:
Vmax = wNBA.
Vmax = wNBA = 100(500)(.5)(.01) = 250Volts.
Lenz’s Law
When an external magnetic field changes through a conducting loop, a current is induced that produces another magnetic field that opposes the external change.
Lenz’s Law
If the B field points in and increases, the current in the loop is…………..
Counter - Clockwise
STARTER
If the B field points into this conducting loop of wireand increases with time, the direction of the current in the loop is…………..
Counter-Clockwise
Transformer EquationsN1 = number of turns on the primary side
N2 = number of turns on the secondary side
V1 = AC voltage applied to the primary side
V2 = AC voltage on the secondary side
I1 =current in the primary windings
I2 = current in the secondary windings
From Faraday’s Law : V2 = V1 (N2/N1)
From conservation of energy: V1 I1 = V2 I2
Then: I2 = I1 (N1/N2)
Transformer Equations
Step Up Transformer N2>N1
Example: A transformer has 5000 turns in the secondary and 1000 turns in the primary.
The primary voltage is 100V (AC) and the primary current is 25 Amps.
1. What is the secondary voltage?2. What is the secondary current?3. What is the power in the primary and
secondary?
Solve the Problem
Givens: V1 = 100 N1 = 1000 N2= 5000
I1 = 25
1. Solve for V2 :
V2 = V1 (N2/N1) = 100( 5000/1000) = 500 Volts
2. Solve for I2:
I2 = I1 (N1/N2) = 25( 1000/5000) = 5 Amps.
3. P1 = P2 : V1 I1 = V2 I2 = 2500 Watts
Step Down Transformer N2<N1
Example: A transformer plugged into the wall ( 120V) charges a 9 volt battery.
1. What is the turn ratio (N1/N2) ?
2. What is the secondary current if the primary current is .5A?
3. What is the power in the primary and secondary?
Solve the Problem
Givens: V1 = 120 V2 = 9 I1 = .5
1. Solve for (N2/N1) :
V2 = V1 (N2/N1) so (N2/N1) = V2 /V1 = 9/120 = .075
2. Solve for I2:
I2 = I1 (N1/N2) = .5 ( 1 /.075) = 6.67Amps.
3. P1 = P2 : V1 I1 = V2 I2 = 60 Watts