To Determine Resistance Of a Galvanometer By Half-

Deflection Method & to Find Its Figure Of Merit

Aim
To determine resistance of a galvanometer by half-deflection method and to find its
figure of merit.

Apparatus
A Weston type galvanometer, a voltmeter, a battery or battery eliminator, two (10,000 Ω
and 200 Ω) resistance boxes, two one-way keys, a rheostat, a screw gauge, a metre
scale, an ammeter of given range, connecting wires and a piece of sand paper.

Theory

Circuit diagram
Procedure
(a) Resistance of galvanometer by half deflection method

1. Make the connections accordingly as shown in circuit diagram.

2. See that all plugs of the resistance boxes are tight.
3. Take out the high resistance (say 2000 Ω) from the resistance box R and insert
the key K1 only.
4. Adjust the value of R so that deflection is maximum, even in number and within
the scale.
5. Note the deflection. Let it be θ.
6. Insert the key also and without changing the value of R, adjust the value of S,
such that deflection in the galvanometer reduces to exactly half the value obtained
in step 5 i.e., θ/2.
7. Note the value of resistance S.
8. Repeat steps 4 to 7 three times taking out different values of R and adjusting S
every time.
(b) Figure of merit
9. Take one cell of the battery (battery eliminator) and find its E.M.F. by a voltmeter
by connecting +ve of the voltmeter with +ve of the cell and -ve of voltmeter with -
ve of the cell. Let it be E.
10. Make connections as in circuit diagram.
11. Adjust the value of R to obtain a certain deflection 0 (say 30 divisions) when the
circuit is closed.
12. Note the values of resistance R and deflection θ.
13. Now change the value of R and note the galvanometer deflection again.
14. Repeat the steps 9 to 13 with both cells of the battery with different voltages like 2,
4, 6, 8, volts from battery eliminator.
15. Find the figure of merit k using the formula.

Observations and Calculations

1. Table for resistance of the galvanometer by half deflection method

 2. Table for figure of merit

Result

1. Resistance of given galvanometer = …….. Ω

2. Figure of merit of given galvanometer = A/dn.

Precautions

1. All the connections should be neat, clean and tight.

2. All the plugs in resistance boxes should be tight.
3. The e.m.f. of cell or battery should be constant.
4. Initially a high resistance from the resistance box (R) should be introduced in the
circuit (otherwise for small resistance an excessive current will flow through the
galvanometer or ammeter can be damaged).
Sources of error

1. The screws of the instruments may be loose.

2. The plugs of resistance boxes may not be clean.
3. The e.m.f. of battery may not be constant.
4. The galvanometer divisions may not be of equal size.
To determine Resistance Per Cm Of a Given Wire by Plotting
a graph Of Potential Difference Versus Current.

Aim
To determine resistance per cm of a given wire by plotting a graph of potential
difference versus current.

Apparatus
A resistance wire, a voltmeter (0-3) V and an ammeter (0-3) A of appropriate range, a
battery (battery eliminator), a rheostat, a metre scale, one way key, connecting wires
and a piece of sand paper.

Theory
According to the Ohm’s law the current flowing through a conductor is directly
proportional to the potential difference across its ends provided the physical conditions
(temperature, dimensions, pressure) of the conductor remains the same. If I be the
current flowing through a conductor and V be the potential difference across its ends,
then according to, Ohm’s Law,

R depends upon the nature of material, temperature and dimensions of the conductor.
In S.I. units, the potential difference V is measured in volt and the current I in ampere,
the resistance R is measured in ohm.
(1) To establish the current-voltage relationship, it is to be shown that the
ratio V/I remains constant for a given resistance, therefore a graph between the
potential difference (V) and the current (I) must be a straight line.
Circuit diagram

Procedure

1. Arrange the apparatus in the same manner as given in the arrangement diagram.
2. Clean the ends of the connecting wires with sand paper to remove the insulations,
if any.
3. Make neat, clean and tight connections according to the circuit diagram. While
making connections ensure that +ve marked terminals of voltmeter and ammeter
are joined towards the +ve terminal of the battery.
4. Determine the least count of voltmeter and ammeter, and also note the zero error,
if any.
5. Insert the key K, slide the rheostat contact and see that ammeter and voltmeter
are
working properly.
6. Adjust the sliding contact of the rheostat such that a measurable current passes
through the resistance coil or the resistance wire.
7. Note down the value of potential difference V” from voltmeter and current I from
ammeter.
8. Shift the rheostat contact slightly so that both ammeter and voltmeter show full
divisions readings and not in fraction.
9. Record the readings of the voltmeter and ammeter.
Note. In case of battery eliminator, follow these steps:
Turn the knob at 2 V in battery eliminator and put the constant point in rheostat at
fixed position. Now record the reading in voltmeter and ammeter.
Without disturbing the rheostat, turn the knob of battery to different voltage such
that 4, 6, 8, 10 and 12 Volts and record corresponding readings in voltmeter and
ammeter.
10. Take at least five sets of independent observations.
 11. Cut the resistance wire at the points where it leaves the terminals, stretch it and
find its length by the metre scale.
12. Record your observations.

Observations

1. Length
Length of the resistance wire l = ……….
2. Range
Range of the given ammeter = ……….
Range of the given voltmeter = ……….
3. Least count
Least count of ammeter = ……….
Least count of voltmeter = ……….
4. Zero error
Zero error in ammeter, e1 = ……….
Zero error in voltmeter, e2 = ……….
 5. Zero correction
Zero correction for ammeter, c1 = -e1 = ……….
Zero correction for voltmeter, c2 = -e2 = ……….
6. Table for Ammeter and Voltmeter
Readings

Calculations
1. Find ratio of V and I for each set of observations.
2. Plot a graph between potential difference V (column 36) and current I (column 26),
taking V along X-axis and I along Y-axis. The graph comes to be a straight line.
Result

1. Resistance per cm of the wire is …….. Ω cm-1.

2. The graph between V and I is a straight line.
Precautions

1. The connections should be neat, clean and tight.

2. Thick copper wires should be used for the connections after removing the
insulations near their ends by rubbing with sand paper.
3. Voltmeter and ammeter should be of proper range.
4. A low resistance rheostat should be used.
5. The key should be inserted only while taking observations to avoid heating of
resistance (otherwise its resistance will increase).

Sources of error

1. The instrument screws may be loose.

2. Thick connecting wires may not be available.
3. Rheostat may have high resistance.
 To Find Resistance Of a Given Wire Using Metre Bridge &
Hence Determine The Resistivity (Specific Resistance)
Of Its Material.

Aim
To find resistance of a given wire using Metre Bridge and hence determine the
resistivity (specific resistance) of its material.

Apparatus
A metre bridge (slide wire bridge), a Leclanche cell (Battery eliminator), a galvanometer,
a resistance box, a jockey, a one way key, a resistance wire, a screw gauge, a metre
scale, a set square, connecting wires and a piece of sand paper.

Theory

(i) The unknown resistance X is given by

where, R is known resistance placed in the left gap and unknown resistance X in the
right gap of metre bridge. I cm is the length of metre bridge wire from zero end upto
balance point.
(ii) Specific resistance (p) of the material of the given wire is given by

where, L is the length and D is the diameter of the given wire.

Circuit diagram

Procedure
For Resistance

1. Arrange the apparatus as shown in arrangement diagram.

2. Connect the resistance wire whose resistance is to be determined in the right gap
between C and B. Take care that no part of the wire forms a loop:
3. Connect resistance box of low range in the left hand gap between A and B.
4. Make all the other connections as shown in the circuit diagram.
5. Take out some resistance (say 2 ohm) from the resistance box, plug the key K.
6. Touch the jockey gently first at left end and then at right end of the bridge wire.
7. Note the deflections in the galvanometer. If the galvanometer shows deflections in
opposite directions, the connections are correct. If the deflection is one side only,
then there is some fault in the circuit. Check or take help of your teacher and
rectify the fault.
8. Move (slide) the jockey gently along the wire from left to right till galvanometer
gives zero deflection. The point where the jockey is touching the wire is null point
D.
 9. Choose an appropriate value of 12 from the resistance box such that there is no
deflection in the galvanometer when the jockey is nearly in the middle of the wire
(i.e. Between 45 cm to 55 cm).
10. Note position of point D (with the help of a set square) to know length AD = l.
11. Take at least four sets of observations in the same way by changing the value of
12 in steps.
12. Record your observations.

For Specific Resistance

13. Cut the resistance wire at the points where it leaves the terminals, stretch it and
find its length by using a metre scale.
14. Measure the diameter of the wire at least at four places, in two mutually
perpendicular directions at each place with the help of screw gauge.
15. Record your observations as given in tables.

Observations
1.Length of given wire L = cm.
1. Length of given wire L = cm.
2. Table for unknown resistance (X)

3. Least count of the screw gauge

4. Table for diameter (D) of the wire

Calculations

Result

1. The value of unknown resistance X =………

2. The specific resistance of the material of the given wire =………
3. Percentage error =……….

Precautions

1. The connections should be neat, clean and tight.

2. All the plugs in the resistance box should be tight.
3. Move the jockey gently over the bridge wire and do not rub it.
4. The plug in key K should be inserted only when the observations are to be taken.
5. Null point should be brought between 45 cm and 55 cm.
6. Set square should be used to note null point to avoid error of parallax.
7. At one place, diameter of wire should be measured in two mutually perpendicular
directions.
 8. The wire should not make a loop.

Sources of error

1. The instrument screws may be loose.

2. The plugs may not be clean.
3. The wire may not have uniform thickness.
4. The screw gauge may have faults like back lash error and wrong pitch.
 To Verify the Laws of Combination (Series) of
Resistances Using a Metre Bridge.

Aim
To verify the laws of combination (series) of resistances using a metre bridge.

Apparatus
A metre bridge, a Leclanche cell (battery eliminator), a galvanometer, a resistance box,
a jockey, two resistance wires or two resistance coils known resistances, a set square,
sand paper and connecting wires.

Theory

where R is the resistance from the resistance box in the left gap and l is the length of
the metre
bridge wire from zero end upto balance point.
Circuit diagram

Procedure
1. Mark the two resistance coils as r 1 and r2.
2. To find r1 and r2 proceed same way as in Experiment 1. (If r 1 and r2 are not known.)
3. Connect the two coils r1 and r2 in series as shown in figure in the right gap of Metre
Bridge and find the resistance of this combination. Take at least three sets of
observations.
4. Record your observations as follows.

Observations
Table for length (1) and unknown resistance (X)
Calculations
1. Calculation for r1 only, r2 r2only, r1 and r2 in series.
Same as in Experiment 1.
2. Calculation for verification of laws Experimental value of R s = ……
Theoretical value of Rs = r1 + r2 = ……
Difference (if any) = ……

Result
Within limits of experimental error, experimental and theoretical values of Rs are same.
Hence, law of resistances in series is verified.

Precautions

1. The connections should be neat, clean and tight.

2. Thick copper wires should be used for the connections after removing the
insulations near their ends by rubbing with sand paper.
3. Voltmeter and ammeter should be of proper range.
4. A low resistance rheostat should be used.
5. The key should be inserted only while taking observations to avoid heating of
resistance (otherwise its resistance will increase).
 To Draw the I-V Characteristic Curve Of a p-n Junction In
Forward Bias & Reverse Bias

Aim
To draw the I-V characteristic curve of a p-n junction in forward bias and reverse
bias.
Apparatus
A p-n junction (semi-conductor) diode, a 3 volt battery, a 50 volt battery, a high
resistance rheostat, one 0-3 volt voltmeter, one 0-50 volt voltmeter, one 0-100 mA
ammeter, one 0-100 μA ammeter, one way key, connecting wires and pieces of sand
paper.

Theory
Forward bias characteristics. When the p -section of the diode is connected to positive
terminal of a battery and n-section is connected to negative terminal of the battery then
junction is said to be forward biased. With increase in bias voltage, the forward current
increases slowly in the beginning and then rapidly. At about 0.7 V for Si diode (0.2 V for
Ge), the current increases suddenly. The value of forward bias voltage, at which the
forward current increases rapidly, is called cut in voltage or threshold voltage.
Reverse bias characteristics. When the p -section of the diode is connected to negative
terminal of high voltage battery and n-section of the diode is connected to positive
terminal of the same battery, then junction is said to be reverse biased.
When reverse bias voltage increases, initially there is a very small reverse current flow,
which remains almost constant with bias. But when reverse bias voltage increases to
sufficiently high value, the reverse current suddenly increases to a large value. This
voltage at which breakdown of junction diode occurs (suddenly large current flow) is
called zener breakdown voltage or inverse voltage. The breakdown voltage may^tarts
from one volt to several hundred volts, depending upon dopant density and the
depletion layer.

Diagram
Procedure

For forward-bias

1. Make circuit diagram as shown in diagram.

2. Make all connections neat, clean and tight.
3. Note least count and zero error of voltmeter (V) and milli-ammeter (mA).
4. Bring moving contact of potential divider (rheostat) near negative end and insert
the key K. Voltmeter V and milli-ammeter mA will give zero reading.
5. Move the contact a little towards positive end to apply a forward-bias voltage (VF)
of
0. 1 V. Current remains zero.
6. Increase the forward-bias voltage upto 0.3 V for Ge diode. Current remains zero,
(It is due to junction potential barrier of 0.3 V).
7. Increase VF to 0.4 V. Milli-ammeter records a small current.
8. Increase VF in steps of 0.2 V and note the corresponding current. Current
increases first slowly and then rapidly, till VF becomes 0.7 V.
9. Make VF = 0.72 V. The current increases suddenly. This represents “forward
break-down” stage.
10. If the VF increases beyond “forward breakdown” stage, the forward current does
not change much. Now take out the key at once.
11. Record your observations as given ahead.
For reverse-bias
12. Make circuit diagram as shown in diagram.
13. Make all connections neat, clean and tight.
14. Note least count and zero error of voltmeter (V) and micro-ammeter (μA).
15. Bring moving contact of potential divider (rheostat) near positive end and insert
the key K Voltmeter V and micro-ammeter μA will give zero reading.
16. Move the contact towards negative end to apply a reverse-bias voltage (VR) of 0.5
V, a feebly reverse current starts flowing.
 17. Increase VR in steps of 0.2 V. Current increases first slowly and then rapidly till
VR becomes 20 V. Note the current.
18. Make VR = 25 V. The current increases suddenly. This represents “reverse break-
down” stage. Note the current and take out the key at once.
19. Record your observations as given ahead.

Observations

For forward-bias
Range of voltmeter = …..V
Least count of voltmeter = …..V
Zero error of voltmeter = …..V
Range of milli-ammeter = …..mA
Least count of milli-ammeter = …..mA
Zero error of milli-ammeter = …..mA

1. Table for forward-bias voltage and forward current

Note. The readings are as a sample.

For reverse-bias
Range of voltmeter = …..V
Least count of voltmeter = …..V
Zero error of voltmeter = …..V
Range of micro-ammeter = …..μA
Least count of micro-ammeter = …..μA
Zero error of micro-ammeter = …..

2. Table for reverse-bias voltage and reverse current

Note. The readings are given as a sample.

Calculations

For forward-bias
Plot a graph between forward-bias voltage VF (column 2) and forward current IF (column
3) taking VF along X-axis and IF along Y-axis. This graph is called forward-bias
characteristic curve a junction diode.
For reverse-bias
Plot a graph between reverse-bias voltage VR (column 2) and reverse current IR (column
3) taking VR along X-axis and IR along Y-axis.
This graph is called reverse-bias characteristic curve of a junction diode.
Result
Junction resistance for forward-bias = 40 ohms
Junction resistance for reverse-bias = 2 x 106 ohms.

Precautions

1. All connections should be neat, clean and tight.

2. Key should be used in circuit and opened when the circuit is not being used.
3. Forward-bias voltage beyond breakdown should not be applied.
4. Reverse-bias voltage beyond breakdown should not be applied.

Sources of error
The junction diode supplied may be faulty.
 To Find the Refractive Index Of a Liquid By Using Convex
Lens & Plane Mirror

Aim

To find the refractive index of a liquid by using convex lens and plane mirror.

Apparatus

A convex lens, a plane mirror, clean transparent liquid in a beaker, an optical needle, (a
thick knitting needle passed through a rubber cork), an iron stand with base and clamp
arrangement, plumb line, plane glass slab, a spherometer, half metre scale etc.

Theory

If f1 and f2 be the focal length of glass convex lens and liquid lens and F be the focal
length of their combination then,

Liquid lens formed is a planoeconcave lens with R 1= R (radius of curvature of convex

lens surface), R2 =∞
Diagram

Procedure

(a) For focal length of convex lens

1. Take any one convex lens and find its rough focal length.
2. Take a plane mirror and place it on the horizontal base of the iron stand.
3. Place the convex lens on the plane mirror.
4. Screw tight the optical needle in the clamp of the stand and hold it horizontally
above the lens at distance equal to its rough focal length.
5. Bring the tip of the needle at the vertical principal axis of the lens, so that tip of the
needle appears touching the tip of its image.
6. Move the needle up and down and remove parallax between tips of the needle
and its image.
7. Measure distance between tip and upper surface of the lens by using a plumb line
and half metre scale.
8. Also measure distance between tip and the surface of its plane mirror.
(b) For focal length of the combination

1. Take a few drops of transparent liquid on the plane mirror and put the convex lens
over it with its same face above as before (A piano concave liquid lens is formed
between plane mirror and convex lens).
2. Repeat steps 6, 7 and 8.
3. Record your observations as given below.

(c) For radius of curvature of convex lens surface

Observations

1. Rough focal length of convex lens =……… cm.

2. Table for distance of needle tip from lens and mirror

Calculations

Precautions
The liquid taken should be transparent.

1. Only few drops of liquid should be taken so that its layer is not thick.
2. The parallax should be removed tip to tip.

Sources of error
Liquid may not be quite transparent.
The parallax may not be fully removed.