# Tangent Galvanometer

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To find Earth's magnetic field

### Text of Tangent Galvanometer

Tangent GalvanometerA tangent galvanometer is an earlymeasuring instrumentused for the measurement ofelectric current. It works by using acompass needle to compare amagnetic fieldgenerated by the unknown current to the magnetic field of the Earth. It gets its name from its operating principle, the tangent law of magnetism, which states that thetangentof the angle a compass needle makes is proportional to the ratio of the strengths of the two perpendicular magnetic fields. It was first described byClaude Pouilletin 1837.A tangent galvanometer consists of a coil of insulated copper wire wound on a circular non-magnetic frame. The frame is mounted vertically on a horizontal base provided with leveling screws. The coil can be rotated on a vertical axis passing through its centre. A compass box is mounted horizontally at the centre of a circular scale. It consists of a tiny, powerful magnetic needle pivoted at the centre of the coil. The magnetic needle is free to rotate in the horizontal plane. The circular scale is divided into four quadrants. Each quadrant is graduated from 0 to 90. A long thin aluminium pointer is attached to the needle at its centre and at right angle to it. To avoid errors due to parallax, a plane mirror is mounted below the compass needle.

TheoryTangent galvanometer is an early measuring instrument for small electric currents. It consists of a coil of insulated copper wire wound on a circular non-magnetic frame. Its working is based on the principle of the tangent law of magnetism. When a current is passed through the circular coil, a magnetic field (B) is produced at the center of the coil in a direction perpendicular to the plane of the coil. The TG is arranged in such a way that the horizontal component of earths magnetic field (Bh) is in the direction of the plane of the coil. The magnetic needle is then under the action of two mutually perpendicular fields. If is the deflection of the needle, then according to tangent law,LetIis the current passing through the coil of radiusawithnturns, then the field generated by the current carrying circular coil is,

Equating (1) and (2), we get,

The left hand side of equation (4) is a constant and is called the reduction factor (K) of the given tangent galvanometer.

Now from equation (3) & (5), the horizontal intensity of earths magnetic field Bh is,

The initial adjustments are done as follows The plane of the coil is made vertical by adjusting the leveling screws. The compass box alone is rotated so that the 90-90 line in the compass box is in the plane of the coil. The T.G as a whole is rotated till the Aluminium pointer reads 0-0. Note down the number of turns in the coil. A suitable current is allowed to pass through the coil. Note down the current as well as the deflection in T.G. Reverse the current and note the deflection again. Repeat the procedure for different values of current. Measure the radius of the coil from its perimeter. Determine the reduction factor and horizontal intensity of earth's magnetic field.

Procedure

1. Place the tangent galvanometer on an inverted wooden box to raise it above the ferrous metal of the laboratory table. Remove all ferrous metal (such as certain mechanical pencils) from the immediate vicinity of the tangent galvanometer. Turn the thumbscrew to free the pointer, but do not raise the pointer so high that it pushes against the glass plate. Orient the instrument so that the pointer reads zero. If the pointer is bent, each end should be equally close to zero.

2. Place the circular level on top of the glass plate. Level the tangent galvanometer by rotating one or more feet. Remove the level some distance from the instrument. If necessary, rotate the box to re-zero the pointer.

3. Refer to the circuit diagram in section IV. Set the VOLTAGE and CURRENT control knobs on the triple-output power supply to zero (full counter-clockwise position). Use a banana plug lead to connect the positive terminal of the ammeter to the positive terminal of the power supply (red banana jack). Connect the negative terminal of the ammeter (0.1-A range) to a clip on the wiring board. Connect the 50 turn binding post of the tangent galvanometer to the same wiring board clip. Connect the common binding post of the tangent galvanometer (the post with no number next to it) to another clip of the wiring board. Connect one fixed terminal of the 50 resistor to the same clip. Use a banana plug lead to connect the other fixed terminal of the 50 resistor to the negative terminal of the power supply (black banana jack). Set the ammeter (with its internal magnet) some distance from the tangent galvanometer. 4. Turn the power supply on and rotate the CURRENT control knob to its far counter-clockwise position. While observing the ammeter, adjust the VOLTAGE control knob until that the tangent galvanometer reads 20o. If the ammeter reading fluctuates noticeably, tighten all connections. Record the current. Repeat for angles of 30o, 40o and 50o. Change the ammeter range, if necessary, to keep it on scale.

5. Reverse the direction of the current through the coil (NOT THROUGH THE AMMETER) and repeat.

6. Change to the 5 turn binding post of the tangent galvanometer and the 1-A range of the ammeter. Replace the 50 resistor by the 5 resistor. Repeat steps 4 and 5.

7. Lock the pointer, but do not move the tangent galvanometer.

8. Use outside calipers and a meter stick to measure the outside diameter of the coil. Measure the actual windings, not the metal frame.

9. Measuring the inside diameter of the windings is a bit more difficult, because the compass is in the way. Also, we must compensate for the thickness of the metal frame. Measure and record the thickness of the metal which makes up the frame. Using the calipers as outside calipers, open them until they span the inside diameter of the metal frame. Place them on the meter stick; read and record the distance.

Observations and calculationsNumber of turns in the coil =.........

Circumference of the coil,2a =........cm

Radius of the coil, a =........cm

Range of Ammeter =..A

Least count of Ammeter =.. A

1. To find the radius of the coil of Tangent GalvanometerS.No.InnerDiameter(d1)(cm)Outerdiameter(d2)(cm)MeanDiameter(d1 + d2)(cm)Meanradius

(cm)

2. To determine the reduction factor of T.G:TrialNo.AmmeterReading (I)A Pointer deflection in degrees

Direct Reverse

1 2 3 4 Mean (degree)tan(degree)K=I/tan (A) BH (T)

Note: Take deflection between 30 and 60 degrees.

Graph

Calculations

Take two points A and B wide apart on the straight line graph. Draw perpendiculars from B on the x-axis and that from A on the y-axis intersecting each other at point C.

Now, Slope of graph = =

So, Slope, = m

Now compute the value of BH by using the relation

BH = = gauss

Result

The value of earths magnetic field by using a tangent galvanometer and measuring current by an ammeter is_________________

Acknowledgement

Iwould like to express my special thanks of gratitude to my Physics teacher, Mrs. Shikha Jain as well as our principal who gave me the golden opportunity to do this wonderful project which also helped me in doing a lot of Research and i came to know about so many new things I am really thankful to them. Secondly i would also like to thank my parents and friends who helped me a lot in finalizing this project within the limited time frame.

ANKUR PALMIA

Certificate

This is to certify that Ankur Palmia (22) student of class 12th B, has completed the project titled To determine the strength of the earths magnetic field during the academic year 2014 2015 towards partial fulfillment of credit for the Physics practical evaluation of CBSE, and submitted satisfactory report, as compiled in the following pages, under my supervision.

Department of PhysicsOxford Sr. Sec. School

AimTo determine the strength of Earths magnetic field using a Tangent Galvanometer.

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