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Objective

To find the focal length of convex mirror using a convex lens.

Material Required

An optical bench with four upright, a knitting needle, a half-meter scale, a convex lens, a convex mirror, a half-meter scale and a mirror holder.

Formula Used

Ray Diagram

Calculation

Result

The focal length of the convex mirror = 23.20

Precautions

• The tips of the needles and the centres of the lens and the mirror should be at the same height.
• The parallax should be removed from tip to tip.
• The distance between the lens and the mirror should be small.
• While adjusting the image needle, the lens and the object needle should not be disturbed.
• The index correction should be carefully recorded and applied.

Sources of Errors

• Parallax was not removed completely.
• The uprights are not perfectly vertical.
• Optical centre, pole of the mirror and the tip of the object needle are not placed in a line.

Objective

To find the value of v for different values of u in case of a concave mirror and to find the focal length.

Apparatus Required

A knitting needle, a half metre scale, an opticle bench with three uprights, two needles and concave mirror with mirror holder.

Formula Used

Ray Diagram

Observations

Calculation

Result

Mean value of focal length, f = 15.0 cm

(as per sign convention the focal length of concave mirror is negative) =- 15.0 cm

Focal length of concave mirror = 15 cm

Precaution

• Tip to tip parallax should be removed between needle and the image of the object needle.
• Index correction for u and u should be properly determined and must be applied.
• All the uprights should be vertical and principal axis of the mirror should be horizontal.
• To locate the position of the image, the eye should be at least 30 cm away from the needle.
• Tips of the needles and the pole of the mirror should be at the same height as that of the pole of the mirror.

Sources of Errors

• The parallax removal may not be perfect.
• The uprights may not be vertical.

Objective:

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

Apparatus Required:

A Weston type galvanometer, a voltmeter, a battery or
battery eliminator, two(10000 ohm and 1000 ohm) resistance boxes, two one-way keys, a rheostat, a screw gauge, a metre scale, an ammeter if given range,
connecting wires and a piece of sand paper.

Formula Used:

a) To find the resistance of galvanometer:

Where,

G is the resistance of the galvanometer

R is the resistance of the resistance box.

S is the shunt resistance.

b) To find the figure of merit:

The figure of merit is current per unit deflection.

Where,

I is the current in the circuit.

k is the figure of merit.

θ is the deflection.

E is the e.m.f. of the cell or battery eliminator.

Circuit Diagram:

Observations :

(a) Resistance of galvanometer by half deflection method: 

(b) The figure of merit:

Least count of voltmeter = 0.01 V
Range of voltmeter = 0-20 V
Zero error of voltmeter = nil

Calculations :

a) Resistance of Galvanometer

b) Figure of merit

Result:

Resistance of given Galvanometer, G = 55.43 Ω

Figure of merit of Given Galvanometer, k= 6.25 x 10¯5 A/div

Precautions:

1. All connections must be neat and tight.
2. Key Kl should be closed after taking out a high resistance from the
resistance box R.
3. The deflection of galvanometer should be large.
4. The emf of cell or battery should be constant.
5. All the plugs in resistance boxes should be tight.

Sources Of Error:

1. The screws of the instruments may be loose.
2. The plugs of resistance boxes may not be clean.
3. The emf of battery may not be constant.
4. The galvanometer divisions may not be of equal size.

Viva Questions

Q.1. Name two devices used for measuring potential difference between two points in an electric field.

Ans. Potentiometer and voltmeter.

Q.2. How do you determine the resistance of the galvanometer?

Ans. By half deflection method.

Q.3. What do you understand by resistance of a galvanometer and can it be determined?

Ans. It is the resistance offered by the coil of the galvanometer to the flow of current through it. It can be found by half deflection method.

Q.4. Which method is being used by The half deflection method. you to determine the resistance of galvanometer?

Ans. The half deflection method.

Q.5. Define current sensitivity of a galvanometer.

Ans. The deflection produced in the galvanometer, when unit current is passed through it, is called current sensitivity of the galvanometer.

Q.6. Why galvanometer is called a moving coil galvanometer?

Ans. In this galvanometer, the coil moves, while the magnet remains fixed.

Q.7. Which part of galvanometer offers resistance?

Ans. Coil of the galvanometer.

Objective

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

Apparatus Required

A metre bridge, a Leclanche cell or 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.

Formula Used

Diagram

Here R₁ = 1 Ω and R₂ = 2 Ω

Calculation

Result

Hence, laws of combination (parallel) of resistance is verified using a metre bridge.

Precautions

• All connections should be neat and tight.
• All the plugs in the resistance box should be tight.
• Clean the connecting wires and the connecting points of metre bridge properly with sandpaper.
• The jockey should be held perpendicular to wire of metre bridge.
• Try to obtain the balance point between 40 cm and 60 cm.
• Move the jockey gently on the wire and do not keep the jockey and the wire in contact for a long time.

Sources of errors

• The keys of the resistance box may not be clean and tight.
• The wire may not be uniformly thick throughout.
• The screws of the instrument may be loose.

Objective : To verify the laws of combination (series) of resistances by using a meter bridge.

Required Apparatus:

A metre bridge, a Leclanche cell (battery eliminator), a galvanometer, a resistance box, a jockey, two resistance wires or two resistance coils of known resistances, a set square, connecting wires, a piece of sandpaper.

Formula Used: 

(i) The resistance r of a resistance wire or coil is given by

Where, R is known resistance placed in the left gap and unknown resistance r in the right gap of the metre bridge. I cm is the length of a metre bridge wire from zero end up to the balance point.

(ii) When r1 and r2 are connected in series, then their combined resistance.

Circuit Diagram:

Observations Table:

Table for unknown resistance

Calculations:

The experimental value of Rs = 6.74 Ω

Theoretical value of Rs = r1 + r2 = 1.91 Ω + 4.79 Ω = 6.70 Ω

Difference ( if any ) = 6.74 Ω – 6.70 Ω = 0.04 Ω

Result:

Within the limits of experimental error, experimental and theoretical values of R are the same. Hence, the law of resistance in series is verified.

Precautions:

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

2. Plugs should be tightly connected in the resistance box.

3. The movement of the jockey should be gentle and it shouldn’t be rubbed.

4. The key K should be inserted only when the observations are to be taken.

5. The null point should be between 30 cm and 70 cm.

6. To avoid the error of parallax, the set square should be used to note the null point.

7. There shouldn’t be any loops in the wire.

Sources Of Error:

1. The screws of the instrument might be loose.

2. The plugs may not be clean.

3. The wire might be of non-uniform diameter.

Objective:

To find the resistance of a given wire/standard resistor using a metre bridge.

Required Apparatus:

A meter bridge, a battery eliminator, a galvanometer meter, a resistance box, a jockey, a one-way key, a resistance wire, and connecting wires.

Formula Used:

Where,
R is known resistance placed in the left gap of the metre bridge.

X is the unknown resistance placed in the right gap of the metre bridge.

L (cm) is the length of the metre bridge wire from zero end up to the balance point.

Circuit Diagram:

Observation Table:

Calculations:

Result

• The value of unknown resistance X is 5.4056 ohm.

Precautions:

• The balance point should lie between 40 cm and 60 cm.
• All connections should be clean and tight.
• Hold the jockey perpendicular to the wire of the metre bridge.
• Move the jockey gently on the wire and do not keep the jockey and wire in contact for a long time.

Sources of Error:

• The key of the resistance box may not be clean and tight.
• The wire may not be uniformly thick throughout.
• The screw of the instruments may be loose.

Viva Question-Answers

Q.1. What is metre bridge? Explain in brief.

Ans. The metre bridge was originally developed by Charles Wheatstone to measure unknown resistance values and as a means of calibrating measuring instruments, voltmeters, ammeters, etc. by the use of a long resistive slide wire.

Q.2. Explain the structure of metre bridge.
Ans. The metre bridge consists of a one metre long wire of uniform cross sectional area fixed on a wooden block. A scale is attached to the block. Two gaps are formed on it by using thick metal strips in order to make the Wheatstone’s bridge. The terminal B between the gaps is used to connect galvanometer and jockey. The metre bridge operates under Wheatstone’s principle.

Q.3. Why is the metre bridge so called?

Ans. It is so because it uses a one metre long wire.

Q.4.When is a Wheatstone bridge most sensitive?

Ans A bridge is most sensitive when the resistances in the four arms of the bridge are of the same order of magnitude.

Q.5 How do you define resistivity or specific resistance of material?

Ans . It is defined as the resistance of a metre long wire of the material and having an area of cross-section 1 m².

Q.6 Does resistance depend upon length and area of cross-section of the material?

Ans. Yes

Q.7. What happens to the resistivity of a semiconductor, if its temperature is increased?

Ans. The resistivity of a semiconductor decreases with the rise of temperature.

Experiment – 1

Objective:

To determine the resistivity of two wires by plotting a graph for potential difference versus current.

Required Apparatus:

Two resistance wires, a voltmeter (0-3)V and an ammeter (0-3 se) A of appropriate range, a battery/battery eliminator, a rheostat, a meter scale, a one-way key, connecting wires, and a screw gauge.

Formula Used:

By Ohm’s law

Where R is the constant of proportionality, it is known as the resistance of the conductor. R depends on the nature of the material, temperature and dimension of the conductor.

 

Specific resistance (ρ) of the material is given by

Where L is the length and D is the diameter of the given wire

Circuit Diagram:

Observations:

• Range of ammeter = (0 – 3) A
• The least count of ammeter = 0.05 A
• Range of voltmeter = (0 -3) V
• The least count of voltmeter = 0.05 V
• The least count of metre-scale (L.C.) =0.1 cm

Zero error, e=0 mm,   Zero correction, c = 0 mm

 

For 1st wire:

Length of the given wire, L= 15 cm = 0.15 m

Observation Table for Resistance

Mean value of resistance, R=

.Table for Diameter of wire:

Calculation for Specific Resistance:

Graph – Potential difference versus Current

For 2nd wire:

Length of the given wire, L= 29cm = 0.29cm

Observation table for Resistance:

Table for Diameter of wire:

Calculation for Specific Resistance:

Graph – Potential difference versus Current:

Result:

• Resistance of first wire from table = 1.04 Ω and from graph 1.05 Ω
• Resistivity of 1st wire=48.98×10–⁸ Ω-m
• Percentage error = 0.04%.
• Resistance of 2nd wire from table = 2.06 Ω and from graph = 2.00 Ω
• Resistivity of 2nd wire     =      50.19×10–⁸ Ω-m
• Percentage error = 2.43%.

Precautions:

1. The connection should be neat clean and tight.
2. Thick connections wire should be used for the connections.
3. The voltmeter and ammeter should be of proper range.
4. A low-resistance rehosteat should be used.
5. The key should be inserted only while taking observation to avoid heating of resistance.
6. At one place, the diameter of the wire should be measured in two mutually perpendicular directions.
7. The wire should not make a loop.

Source of Error:

1. The instrument crew may be lose.
2. Thick connection wires may not be available.
3. Rehosteat may have high resistance.
4. The wire may not have uniform thickness.
5. The screw gauge may have faults like a ‘back lash’ error and a wrong pitch.