Figure 1
When an alternating current is passed through a coil, a changing magnetic field is produced. This magnetic field is proportional to the number of turns of the coil. For an infinite solenoid the magnetic field B is given by: đ??ľ=
đ?œ‡đ?‘œ đ?‘ đ??ź â„“
(1)
Where: Îźo = The permeability of free space (the magnetic constant) N = The number of turns of the wound coil I = The current through the solenoid â„“ = The length of the solenoid If we have two coils with different numbers of turns, N1 and N2, we can pass a current through one coil and use the resulting fluctuating magnetic field to induce an electromotive force in the second coil by placing it in the vicinity of this magnetic field. Using Faraday’s Law the resulting electromotive force is equal to: đ?œ€ = −đ?‘
Where: N = The number of turns of the coil.
âˆ†ÎŚ ∆đ?‘Ą
(2)
=ď€ ď€ The electromotive force (EMF) induced in the coil.ď€ ÎŚ = The magnetic flux through the coil. Ć?
Assuming that all the magnetic flux created by the first (primary) coil flows through the second (secondary) coil we get the transformer equation: đ?œ€1 đ?‘ 1 = đ?œ€2 đ?‘ 2
(3)
Where Ć?1 and N1 are the electromotive force and number of turns of the primary coil, through which the current is passed. Ć?2 and N2 are the electromotive force and number of turns of the secondary coil, in which the electromotive force is induced. In this activity we will investigate Equation (3).
einstein™Tablet + with MiLAB or Android/iOS Tablet with MiLAB and einstein™LabMate Voltage sensor (¹25 V) Voltage sensor (¹2.5 V) Signal generator Power supply Coil (400 turns) Coil (1600 turns) Armature U core with armature Banana cords (2)
1.
Launch MiLAB (
2.
Connect the ¹2.5 Voltage sensor to one of the ports on the einstein™Tablet+ or einstein™LabMate then connect the banana plugs to the 400 turns coil (primary coil).. Connect the ¹25 Voltage sensor to one of the ports on the einstein™Tablet+ or einstein™LabMate then connect the banana plugs to the 1600 turns coil (secondary coil). Assemble the equipment as shown in Figure 1. a. Use the banana cords to connect the 400 turns coil (primary coil) to the power output of the signal generator. b. Place the 1600 turns coil (secondary coil) next to the primary coil. Make sure that only the two Voltage sensors are selected.
3. 4.
5.
).
Program the sensors to log data according to the following setup: Voltage Sensor (ď‚ą2.5 V)
Voltage (V)
Set As Zero
ON
Voltage Sensor (25 V)
Voltage (V)
Set As Zero
ON
Rate:
100/sec
Duration:
20 Sec
1.
Turn on the signal generator and set it to: Output voltage: ~2 V Frequency: Waveform:
5 Hz Sinusoidal
2.
Tap Run (
) on the main toolbar to begin recording data.
3.
After a couple of seconds tap Stop (
4.
Save your data by tapping Save (
). ).
5.
Use the cursors to measure the voltage drops across the primary and secondary coils. Record the values in your notebook. 6. Insert the armature into both the coils and repeat steps 2 to 5. 7. Mount the coils on the U core and close it with the armature and repeat the experiment.. 8. Repeat steps 2 to 5. 9. Set the signal generator's frequency to 50 Hz and increase the data logger's recording rate to 1000 samples per second. 10. Repeat steps 2 to 5.
For more information on working with graphs see: Working with Graphs in MiLAB. 1. 2. 3. 4. 5.
How did the readings change after inserting the armature? What was the effect of mounting the coils on the U core? Explain the role of the core. Compare the functioning of the transformer in 5 Hz to its functioning in 50 Hz. Do your results agree with Equation (3)? Explain.