PhysicsLAB Resource Lesson
Meters: Current-Carrying Coils

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Solenoids
 
A coil of current-carrying wire is otherwise known as a solenoid; it is often referred to as an electromagnet. The right-hand curl rule for solenoids states that your fingers curve in the direction in which the current flows through the coils while your thumb points in direction of the coil's magnetic moment , or the "N pole" of an electromagnet.
     
 
The right diagram shows a cross-section of the same coil. The black circles  represent where the current is flowing out of the coil and the black  represent where it flows into the coils. Using the right hand curl rule results in your fingers curling up towards you at the top of diagram and down in towards your wrist at the bottom. Consequently your thumb, the North Pole, or magnetic moment of this solenoid, must point down and to the right. Remember that magnetic field lines emerge from the North Pole and circle back into the South Pole.
 
We can use the following physlet to examine more closely the magnetic field inside of a solenoid. In the screen captures shown below, the "red" dots represent currents coming out of the plane of the page (+z) and the "blue" dots represent currents going into the plane of the page (-z). Thus, the right hand curl rule tells us that the magnetic moment, or North Pole, of this solenoid is located on its right side. Note that the magnetic field down the length of the solenoid is uniform and almost identical to that of a bar magnet.
 
 
 
The formula used to calculate the magnetic field within a solenoid is
 
Bsolenoid = µonI

where
 
  • µo = 4π x 10-7 N/A2
  • n represents the ratio of the number of loops per unit length of the solenoid = N/L
 
 
Refer to the following information for the next question.

A long solenoid has 3000 turns on its 60-cm length. The inner diameter of the solenoid is 3 cm.
 Find the strength of the magnetic field within the solenoid when it carries a current of 500 mA.

Ammeters
 
A device which uses the interaction between the magnetic moment of a current-carrying coil and the field of a permanent horseshoe magnet to detect the presence of current through the coil is called a galvanometer. This very sensitive meter movement can then be incorporated into other detection devices to quantitatively determine either the current through or voltage across various sections of an electrical circuit.

Shown on the left is a picture of the demonstration galvanometer I inherited when I began teaching at Mainland in 1975. Although the springs are broken, you can still see the permanent horseshoe magnet, the current coil, and the needle which, when deflected, gauged the amount of current flowing through the coil.
 
To adapt a standard galvanometer movement into use as an ammeter you must place a low resistance shunt in parallel with the galvanometer’s meter movement.
 
 
Since the shunt is in parallel with the galvanometer’s meter movement, it will have the same voltage as the galvanometer. In addition, since it is in parallel, all the excess current will flow through the shunt to protect the galvanometer's meter movement. When you solve for the shunt's resistance r using Ohm's Law,
 
Vmeter movement = Ishuntr
 
its value will be VERY SMALL.
 
 
Refer to the following information for the next five questions.

A certain meter movement has a resistance of 40 ohms and deflects full scale when a voltage of 200 mV is placed across its terminals. The following questions are designed to help you determine how it can be made into a 3-A ammeter.
 What is the maximum current that the coil can tolerate?

 How much of the 3-A current would need to be diverted through a low-resistance shunt resistor?

 What would be the voltage across the shunt resistor?

 What must be the resistance of the shunt resistor?

 Describe your final configuration.

Voltmeters
 
To adapt a standard galvanometer movement into use as a voltmeter, a high resistance multiplier is placed in series with the galvanometer's meter movement.
 
 
Since the multiplier is in series with the galvanometer movement, it will draw the same current as the galvanometer. Being in series allows the multiplier to bleed off the excess voltage to protect the galvanometer. Once again, Ohm's Law would be used to solve for the resistance of this high resistance multiplier,
 
V = Imeter movementR.
 
Refer to the following information for the next five questions.

A certain meter movement has a resistance of 40 ohms and deflects full scale when a current of 0.01 A is run through it. The following questions are designed to help you determine how it can be made into a 15-V voltmeter.
 What is the maximum voltage that the coil can tolerate?

 How much of the 15-V potential difference would need to be bleed off across a high-resistance multiplier?

 What would be the current through the high-resistance multiplier?

 What must be the resistance of the high-resistance multiplier?

 Describe your final configuration.



Usage and placement in circuits
 
When using a voltmeter and an ammeter in a circuit to take measurements, the ammeter would be placed "in line" with the resistor whose current you need to measure, while the voltmeter would be placed "across" the resistor to measure its voltage.
 
 
Notice that the way "to use" each of these devices is EXACTLY the opposite as the way in which they are built from a standard galvanometer movement. These devices only work when current is being drawn through the circuit. Hence, they cause the resistors to heat up and change their resistance. A more efficient means of measuring resistance is to use a Wheatstone Bridge, which when balanced, draws no current through the resistors.

 
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