Experiment Name
Measurement of diameter and area of a circular rigid wire using Screw Gauge.
What is Screw Gauge?
The screw gauge is an instrument used for measuring accurately the diameter of a thin wire or the
thickness of a sheet of metal. It consists of a U-shaped frame fitted with a screwed spindle which is
attached to a thimble.
Parallel to the axis of the thimble, a scale graduated in mm is engraved. This is called pitch scale. A sleeve is
attached to the head of the screw.
The head of the screw has a ratchet which avoids undue tightening of the screw. On the thimble there is a
circular scale known as head scale which is divided into 50 or 100 equal parts. When the screw is worked,
the sleeve moves over the pitch scale.
A stud with a plane end surface called the anvil is fixed on the ‘U’ frame exactly opposite to the tip of the
screw. When the tip of the screw is in contact with the anvil, usually, the zero of the head scale coincides
with the zero of the pitch scale.
Principle
Pitch of the Screw Gauge
The pitch of the screw is the distance moved by the spindle per revolution. To find this, the distance
advanced by the head scale over the pitch scale for a definite number of complete rotation of the screw is
determined.
The pitch can be represented as;
Least Count of the Screw Gauge
The Least count (LC) is the distance moved by the tip of the screw, when the screw is turned through 1
division of the head scale.
The least count can be calculated using the formula;
Principle
Formula for determining the diameter by using Screw Gauge
= Pitch scale reading + Circular scale reading × Least Count-Instrumental error
=L+C× L.C-(±e)
(3)
Area of a circular rigid wire, A= 𝜋𝑟 2
=𝜋
1
4
𝑑 2
2
= 𝜋𝑑2
(4)
Instrument
1. Screw Gauge (Micrometer)
2. Circular rigid wire
Procedure
1. Determine the pitch and least count of the screw gauge using the equations (1) and
(2) respectively.
Procedure
Head scale reading
Procedure
2. Bring the anvil and screw in contact with each other and find the zero error. Do it three
times and record them. If there is no zero error, then record ‘zero error nil’.
Zero Error and Zero Correction
• To get the correct measurement, the zero error must be taken into account. For this purpose, the
screw is rotated forward till the screw just touches the anvil and the edge of cap is on the zero
mark of the pitch scale. The Screw gauge is held keeping the pitch scale vertical with its zero
down wards.
When this is done, anyone of the following three situations can arise:
• The zero mark of the circular scale comes on the reference line. In this case, the zero error and
the zero correction, both are nil.
• The zero mark of the circular scale remains below the reference line and does not cross it. In
this case, the zero error is positive and the zero correction is negative depending on how many
divisions it is above the reference line.
• The zero mark of the head scale is above the reference line. In this case, the zero error is
negative and the zero correction is positive depending on how many divisions it is below the
reference line.
Procedure
3. Move the screw away from the anvil and place the wire and move the screw towards
the anvil using the ratchet head. Stop when the ratchet slips without moving the screw.
Procedure
4. Note the number of divisions on the pitch scale that is visible and uncovered by the
edge of the cap. The reading L is called the pitch scale reading (PSR).
Procedure
5. Note the number (C) of the division of the circular scale (Head scale) lying over
the reference line.
Procedure
6. Repeat steps 3 to 5 for four different positions and record the
observations in the tabular column.
7. Find total reading using the equation 3 and apply zero correction in each
case.
8. Now find the area of a rigid circular wire using the equation (4) by using
the measured values.
Observation
Table: Measuring diameter of a given rigid circular wire.
SI No
1.
2.
3.
4.
Pitch Scale
Reading
L mm
Circular
Scale Count
C (div)
Least
Count
L.C mm
Circular Scale Diameter Mean
Instrumental
Reading
d´=L+F
Diameter Error
F=C×L.C mm mm
d´´ mm
±e mm
Measured
Diameter
d={d´´-(±e) }mm
Calculation
1. Determination of Least Count of the Screw Gauge
1 Linear Scale Division, LSD = 1 mm
Number of full rotations given to screw =4
Distance moved by the screw = 4mm
Hence , pitch p =
= 1mm
Number of divisions on circular scale=100
Hence, least count, L.C =
= 0.01 mm
2. Zero Error
(i) zero error = --------------mm
(ii) zero error = ---------------mm
(iii) zero error = ----------------mm
Mean zero error, e= ------------mm
Mean zero correction , c= -e = -------mm
Calculation
3. Area
Mean Diameter of the given rigid circular wire=---------mm
Area of the given rigid circular wire =
1
𝜋𝑑2
4
=……..mm2
=………cm2
Result
By using Screw Gauge the diameter of the given rigid circular wire = ……………. cm
and the area of the given rigid circular wire = ……………. cm2
Precautions
1. Ratchet arrangement in screw gauge must be utilized to avoid undue
pressure on the wire as this may change the diameter.
2. Move the screw in one direction else the screw may develop “play”.
3. Screw should move freely without friction.
4. Reading should be taken at least at four different points of the wire.
5. View all the reading keeping the eye perpendicular to the scale to
avoid error due to parallax.
Discussion
Try to assess if the value of diameter obtained by
you is realistic or not. There may be an error by a
factor of 10 or 100 . You can obtain a very rough
estimation of the diameter of the wire by measuring
its thickness with an ordinary meter scale.