Class 12 Physics Notes Chapter 2 (Chapter 2) – Lab Manual (English) Book

Detailed Notes with MCQs of the practical aspects of Current Electricity as covered in Chapter 2 of your Lab Manual. These experiments are crucial not just for your practical exams but also form the basis for many conceptual questions in competitive government exams. Pay close attention to the principles, procedures, and especially the precautions and sources of error.

Chapter 2: Current Electricity Experiments - Detailed Notes

This chapter primarily deals with verifying fundamental laws and determining electrical properties using specific apparatus.

1. Ohm's Law Experiment

• Aim: To determine the resistance per unit length of a given wire by plotting a graph of potential difference (V) versus current (I).
• Apparatus: A resistance wire, voltmeter (0-3V), ammeter (0-3A), battery eliminator or battery, rheostat, plug key, connecting wires, sandpaper, metre scale.
• Theory: Ohm's Law states that at constant temperature and other physical conditions, the current (I) flowing through a conductor is directly proportional to the potential difference (V) across its ends.
  • Mathematically: V ∝ I or V = RI
  • Where R is the constant of proportionality called Resistance. Its SI unit is Ohm (Ω).
  • Resistance (R) depends on the material, length (L), and area of cross-section (A) of the conductor: R = ρ (L/A), where ρ is the resistivity (or specific resistance) of the material.
  • A graph plotted between V (on y-axis) and I (on x-axis) should be a straight line passing through the origin. The slope of this graph gives the resistance R (Slope = ΔV / ΔI = R).
• Circuit Diagram:
  • [Draw a simple circuit diagram showing the battery, key, rheostat, ammeter connected in series with the resistance wire. The voltmeter is connected in parallel across the resistance wire.]
  • Key Connections: Ammeter in series, Voltmeter in parallel across the component whose resistance is to be measured. Rheostat controls the current.
• Procedure Summary:
  1. Clean the ends of connecting wires using sandpaper.
  2. Assemble the circuit as per the diagram. Ensure correct polarity of ammeter and voltmeter.
  3. Insert the key. Adjust the rheostat slider so that a small current flows.
  4. Record the readings of the ammeter (I) and voltmeter (V).
  5. Shift the rheostat slider slightly to change the current and record the new set of V and I readings. Obtain 5-6 sets of readings.
  6. Plot a graph with V along the y-axis and I along the x-axis.
  7. Calculate the slope of the graph, which gives the resistance R.
  8. Measure the length (L) of the resistance wire used.
  9. Calculate resistance per unit length (R/L).
• Observations:
  • Length of the resistance wire, L = ... cm = ... m
  • Least count of Ammeter = ... A
  • Least count of Voltmeter = ... V
  • Zero error of Ammeter = ... A
  • Zero error of Voltmeter = ... V
  • Observation Table:

    S.No.	Ammeter Reading (I) (A)	Voltmeter Reading (V) (V)	R = V/I (Ω)
    1
    2
    ...
    Mean R

• Calculations:
  • From graph: Slope = R = (V₂ - V₁) / (I₂ - I₁) = ... Ω
  • Resistance per unit length = R / L = ... Ω/m (or Ω/cm)
• Result: The resistance per unit length of the given wire is found to be ... Ω/m. The V-I graph is a straight line, verifying Ohm's Law.
• Precautions:
  1. Connections should be tight and clean.
  2. Use thick connecting wires.
  3. Ensure correct polarity while connecting the ammeter and voltmeter.
  4. The key should be inserted only while taking readings to avoid unnecessary heating of the wire (which changes its resistance).
  5. Use a low-resistance rheostat.
  6. Record readings starting from low current to high current.
• Sources of Error:
  1. Loose connections.
  2. Heating of the resistance wire.
  3. Non-uniform area of cross-section of the wire.
  4. Instrumental errors (zero error).
  5. Including the resistance of connecting wires (usually negligible).

2. Metre Bridge Experiments

• Principle: The metre bridge works on the principle of the Wheatstone bridge. When the bridge is balanced (current through the galvanometer is zero), the ratio of resistances in the adjacent arms is equal.

  • Wheatstone Bridge Condition: P/Q = R/S
  • In a metre bridge, P and Q are resistances of the bridge wire segments, R is a known resistance (from resistance box), and S is the unknown resistance. If the balancing length from one end (say, left) is 'l' cm, then P ∝ l and Q ∝ (100 - l).
  • Therefore, (Resistance of length l) / (Resistance of length (100-l)) = R / S
  • Assuming the wire has uniform resistance per unit length, this simplifies to: l / (100 - l) = R / S
  • Hence, the unknown resistance S = R * (100 - l) / l

• Apparatus: Metre bridge, galvanometer, resistance box, unknown resistance wire (S), jockey, battery/eliminator, plug key, connecting wires, sandpaper, screw gauge, metre scale.

  (A) To find the resistance of a given wire and determine the specific resistance (resistivity) of its material.

  • Aim: As stated above.
  • Theory: S = R * (100 - l) / l. Specific Resistance (Resistivity) ρ = S * A / L = S * (πr²) / L, where r is the radius and L is the length of the unknown resistance wire.
  • Circuit Diagram: [Draw the standard metre bridge circuit: Battery and key connected across the ends of the metre bridge wire. One gap contains the Resistance Box (R), the other contains the Unknown Resistance (S). Galvanometer connected between the central terminal (junction of R and S) and the jockey.]
  • Procedure Summary:
    1. Set up the circuit. Clean wire ends.
    2. Take out a suitable resistance (R) from the resistance box.
    3. Touch the jockey near the left end (A) and then near the right end (C) of the wire. The galvanometer deflection should be in opposite directions.
    4. Slide the jockey gently along the wire to find the null point (D) where the galvanometer shows zero deflection. Record the balancing length AD = l cm.
    5. Repeat for different values of R, obtaining 3-4 sets of readings.
    6. Measure the length (L) of the unknown resistance wire using a metre scale.
    7. Measure the diameter (D) of the wire using a screw gauge at several points and find the mean radius (r = D/2).
  • Observations:
    • Length of unknown wire L = ... m
    • Screw Gauge Measurements (for diameter D, radius r)
    • Observation Table:

      S.No.	Resistance from RB (R) (Ω)	Balancing Length (l) (cm)	(100 - l) (cm)	S = R(100-l)/l (Ω)
      1
      2
      ...
      Mean S

  • Calculations: Calculate mean S. Calculate area A = πr². Calculate ρ = S * A / L.
  • Result: Unknown Resistance S = ... Ω. Specific Resistance ρ = ... Ωm.
  • Precautions & Sources of Error for Metre Bridge (Common to both parts):
    1. Connections must be tight.
    2. Clean the plugs of the resistance box and wire ends.
    3. Do not slide the jockey harshly; press it gently. Sliding can scrape the wire, making its cross-section non-uniform.
    4. The balancing point should preferably be between 40 cm and 60 cm for higher accuracy (minimizes percentage error in l and 100-l). Adjust R accordingly.
    5. Switch off the current when readings are not being taken.
    6. Check for opposite deflections at the ends before finding the null point.
    7. Repeat measurements by interchanging R and S positions in the gaps to minimize end errors. Calculate the mean S.
    • Sources of Error: Non-uniformity of the bridge wire, end resistances (resistance of the copper strips and points where the wire is soldered - called end correction), heating effect, galvanometer sensitivity issues, backlash error in screw gauge.

  (B) To verify the laws of combination (Series/Parallel) of resistances.

  • Aim: As stated above.
  • Theory:
    • Series Combination: R_s = R₁ + R₂
    • Parallel Combination: 1/R_p = 1/R₁ + 1/R₂ or R_p = (R₁ * R₂) / (R₁ + R₂)
  • Procedure Summary:
    1. Take two resistance wires/coils (R₁ and R₂).
    2. Find the resistance of R₁ individually using the metre bridge method (as in part A). Let this be R₁ (experimental).
    3. Find the resistance of R₂ individually. Let this be R₂ (experimental).
    4. Connect R₁ and R₂ in series and find their combined resistance using the metre bridge. Let this be R_s (experimental).
    5. Connect R₁ and R₂ in parallel and find their combined resistance. Let this be R_p (experimental).
    6. Calculate the theoretical values: R_s (theoretical) = R₁ + R₂ and R_p (theoretical) = (R₁ * R₂) / (R₁ + R₂), using the experimentally found individual resistances.
    7. Compare the experimental and theoretical values for series and parallel combinations.
  • Observations & Calculations: Record balancing lengths and calculate R₁, R₂, R_s, R_p. Compare experimental and theoretical values and find the percentage difference.
  • Result: The experimental and theoretical values for series and parallel combinations are found to be approximately equal, thus verifying the laws of combination.

3. Potentiometer Experiments

• Principle: A potentiometer works on the principle that the potential drop (V) across any portion of a uniform wire carrying a constant current (I) is directly proportional to the length (l) of that portion.

  • V ∝ l or V = kl
  • Where k is the potential gradient (potential drop per unit length) along the potentiometer wire. k = V_wire / L_wire.
  • Condition: The wire must be of uniform area of cross-section, and the current through it must remain constant.

• Apparatus: Potentiometer, battery (driver cell), two primary cells (Leclanche, Daniel), rheostat, galvanometer, high resistance box (HRB), plug keys (one-way and two-way), jockey, connecting wires, sandpaper.

  (A) To compare the EMFs of two given primary cells.

  • Aim: As stated above.
  • Theory: When a cell of EMF E is balanced against a length 'l' of the potentiometer wire, the potential drop across length 'l' is equal to the EMF of the cell (since no current is drawn from the cell at balance).
  • E = kl
  • For cell E₁: E₁ = kl₁
  • For cell E₂: E₂ = kl₂
  • Dividing the two equations (assuming k is constant): E₁ / E₂ = l₁ / l₂
  • Condition: The EMF of the driver cell must be greater than the EMFs of the cells being compared.
  • Circuit Diagram: [Draw the potentiometer circuit. Primary circuit: Driver battery, key, rheostat connected across the potentiometer wire ends (A, B). Secondary circuit: Positive terminals of E₁ and E₂ connected to A. Negative terminals connected through a two-way key to the galvanometer, which is then connected to the jockey. Ensure positive terminals of driver cell and experimental cells are connected to the same point A.]
  • Procedure Summary:
    1. Set up the circuit. Ensure correct polarity.
    2. Adjust the rheostat in the primary circuit to get a suitable potential gradient. Check if the balance point for the cell with higher EMF lies on the last wire segment.
    3. Insert the plug for cell E₁ (using the two-way key). Find the balancing length l₁ from end A.
    4. Remove the plug for E₁ and insert it for cell E₂. Find the balancing length l₂ from end A without changing the rheostat setting.
    5. Repeat for different rheostat settings (different k values).
  • Observations:

    S.No.	Balancing length for E₁ (l₁) (cm)	Balancing length for E₂ (l₂) (cm)	E₁ / E₂ = l₁ / l₂
    1
    2
    ...
    Mean Ratio

  • Calculations: Calculate the mean ratio E₁ / E₂.
  • Result: The ratio of EMFs of the two given cells E₁ / E₂ = ...
  • Precautions & Sources of Error for Potentiometer (Common to both parts):
    1. The EMF of the driver cell must be greater than the EMFs of the experimental cells.
    2. All positive terminals should be connected to the same end (A) of the potentiometer.
    3. The current in the potentiometer wire (primary circuit) should remain constant throughout the experiment for a given set of readings. Use a freshly charged accumulator.
    4. Do not slide the jockey; press it gently.
    5. Use a high resistance box initially in series with the galvanometer to protect it from large currents when far from the balance point. Short the HRB near the balance point for accuracy.
    6. The potentiometer wire should be of uniform cross-section and material.
    • Sources of Error: Non-uniformity of wire, variation in driver cell current/EMF, incorrect measurement of balancing length, end resistances, potential gradient not being constant.

  (B) To determine the internal resistance of a given primary cell.

  • Aim: As stated above.
  • Theory: The internal resistance (r) of a cell is given by:
    • r = R * ( (E - V) / V )
    • Using the potentiometer principle, E ∝ l₁ (balancing length when the cell is in open circuit - no current drawn from it).
    • The terminal potential difference V ∝ l₂ (balancing length when the cell sends current through an external resistance R connected across its terminals).
    • Therefore, r = R * ( (l₁ - l₂) / l₂ )
  • Circuit Diagram: [Primary circuit same as before. Secondary circuit: Positive terminal of the experimental cell (E) connected to A. Negative terminal connected to the galvanometer (via HRB) and jockey. A resistance box (R) and a plug key (K₂) are connected in parallel across the terminals of cell E.]
  • Procedure Summary:
    1. Set up the circuit. Keep key K₂ open.
    2. Find the balancing length l₁ corresponding to the EMF (E) of the cell.
    3. Introduce a suitable resistance (R) from the resistance box and close key K₂. The cell now sends current through R.
    4. Find the new balancing length l₂ corresponding to the terminal potential difference (V) of the cell. Ensure l₂ < l₁.
    5. Repeat for different values of R.
  • Observations:

    S.No.	Resistance from RB (R) (Ω)	Balancing length (K₂ open) l₁ (cm)	Balancing length (K₂ closed) l₂ (cm)	r = R(l₁-l₂)/l₂ (Ω)
    1
    2
    ...
    Mean r

  • Calculations: Calculate mean internal resistance r.
  • Result: The internal resistance of the given primary cell is r = ... Ω.

4. Galvanometer Resistance by Half-Deflection Method & Figure of Merit

• Aim: To determine the resistance of a galvanometer (G) by half-deflection method and to find its figure of merit (k).
• Apparatus: Galvanometer, battery, two resistance boxes (one high resistance R, one low resistance S), two one-way keys, connecting wires, sandpaper.
• Theory:
  • Resistance (G):
    1. A high resistance (R) is connected in series with the galvanometer and battery to get a deflection θ (say, full scale or a large even number). Current I = E / (R + G). Since R >> G, approximately I ≈ E / R. Deflection θ ∝ I.
    2. A low resistance shunt (S) is connected in parallel with the galvanometer. The value of S is adjusted such that the galvanometer deflection becomes half (θ/2).
    3. In the half-deflection condition, the potential difference across G and S is the same. Also, the current through G is now I_g = I/2 (approximately, if R is very large). The current divides between G and S.
    4. Applying current division rule or Kirchhoff's laws, it can be shown that if R is very large compared to G, then G ≈ S.
    5. A more accurate formula (without approximation) is G = (R * S) / (R - S).
  • Figure of Merit (k): It is the current required to produce a deflection of one division in the galvanometer scale.
    • k = I_g / θ
    • From the initial circuit (without shunt S), the current causing deflection θ is I = E / (R + G).
    • So, k = E / ((R + G) * θ) (Amperes per division).
• Circuit Diagram:
  • [Circuit 1 (for G): Battery, Key K₁, High Resistance Box (R), Galvanometer (G) in series. Key K₂ and Shunt Resistance Box (S) connected in parallel across G.]
  • [Circuit 2 (for k): Battery, Key K₁, High Resistance Box (R), Galvanometer (G) in series. (Essentially the first part of Circuit 1 before adding the shunt).]
• Procedure Summary:
  1. For G: Connect Circuit 1. Take out a high resistance R (e.g., 5000 Ω) from RB₁. Close K₁. Adjust R until the galvanometer shows a large even deflection θ (e.g., 30 divisions). Record R and θ. Close K₂. Adjust the shunt resistance S from RB₂ until the deflection reduces to θ/2. Record S. Repeat for different θ values. Calculate G ≈ S or use G = RS/(R-S).
  2. For k: Use Circuit 2 (or Circuit 1 with K₂ open). Note the EMF (E) of the battery. Close K₁. Adjust R to get a measurable deflection θ. Record R and θ. Calculate k = E / ((R + G) * θ), using the value of G found earlier. Repeat for different R values.
• Observations: EMF E = ... V. Least count of Galvanometer = ... div.
  • Table for G:

    S.No.	R (Ω)	Deflection θ (div)	Shunt S (Ω) for θ/2	G ≈ S (Ω)	G = RS/(R-S) (Ω)
    1
    ...
    Mean G

  • Table for k:

    S.No.	R (Ω)	Deflection θ (div)	k = E/((R+G)θ) (A/div)
    1
    ...
    Mean k

• Calculations: Calculate mean G and mean k.
• Result: Galvanometer Resistance G = ... Ω. Figure of Merit k = ... A/div.
• Precautions:
  1. Use high resistance R initially.
  2. Ensure deflections are large and easily readable.
  3. Key K₂ should be closed only after adjusting R for initial deflection θ.
  4. Value of S should be small compared to G.
• Sources of Error: Approximation G ≈ S is valid only if R >> S. EMF of battery may not be constant.

5. Conversion of Galvanometer

• Aim: To convert a given galvanometer (of known resistance G and figure of merit k) into (a) an ammeter of desired range (0-I A) and (b) a voltmeter of desired range (0-V V), and to verify the conversion.
• Apparatus: Galvanometer, battery, rheostat, ammeter (for verification), voltmeter (for verification), two resistance boxes, keys, connecting wires.
• Theory:
  • Conversion to Ammeter: An ammeter measures current and is connected in series. It must have very low resistance. This is achieved by connecting a low resistance shunt (S) in parallel with the galvanometer.
    • Let I_g be the current for full-scale deflection (FSD). I_g = n * k, where n is the total number of divisions on the galvanometer scale.
    • If the desired range is I, the shunt must carry current (I - I_g).
    • Since G and S are in parallel, potential difference is the same: I_g * G = (I - I_g) * S
    • Shunt Resistance required: S = (I_g * G) / (I - I_g)
  • Conversion to Voltmeter: A voltmeter measures potential difference and is connected in parallel. It must have very high resistance. This is achieved by connecting a high resistance (R) in series with the galvanometer.
    • For FSD current I_g, the total resistance should be (R + G).
    • If the desired range is V, then according to Ohm's law: V = I_g * (R + G)
    • Series Resistance required: R = (V / I_g) - G
• Circuit Diagram:
  • [Diagram 1: Conversion to Ammeter - Galvanometer with calculated shunt S in parallel. This combination acts as the ammeter.]
  • [Diagram 2: Verification of Ammeter - Battery, key, rheostat, standard ammeter, and the converted galvanometer (G || S) connected in series.]
  • [Diagram 3: Conversion to Voltmeter - Galvanometer with calculated resistance R in series. This combination acts as the voltmeter.]
  • [Diagram 4: Verification of Voltmeter - Battery, key, rheostat connected across a load resistance. Standard voltmeter and the converted galvanometer (G + R in series) connected in parallel across the load resistance.]
• Procedure Summary:
  1. Note G, k, n (number of divisions). Calculate I_g = nk.
  2. Ammeter: Calculate required shunt S for desired range I using S = (I_g * G) / (I - I_g). Connect this resistance S (using a resistance box or wire) in parallel with G. Verify using Circuit 2 by varying the rheostat and comparing the reading of the converted ammeter (deflection * current per division) with the standard ammeter reading.
  3. Voltmeter: Calculate required series resistance R for desired range V using R = (V / I_g) - G. Connect this resistance R (using a resistance box) in series with G. Verify using Circuit 4 by varying the rheostat and comparing the reading of the converted voltmeter (deflection * voltage per division) with the standard voltmeter reading.
• Observations & Calculations: Record calculated S and R. Create verification tables comparing standard instrument readings with converted instrument readings. Calculate error if any.
• Result: The calculated values of S and R convert the galvanometer into an ammeter and voltmeter of the desired ranges, as verified experimentally.
• Precautions:
  1. Calculate S and R accurately.
  2. Use standard instruments (ammeter, voltmeter) of appropriate ranges for verification.
  3. Ensure tight connections.
  4. Do not exceed the current/voltage limits of the galvanometer or the standard instruments.
• Sources of Error: Error in G and k values, resistance of connecting wires, least count errors of instruments, contact resistances.

Multiple Choice Questions (MCQs)

1. In the experiment to verify Ohm's law, the graph between potential difference (V) and current (I) is a straight line. The slope of this graph represents:
   a) Resistivity
   b) Resistance
   c) Conductance
   d) Potential Gradient

2. A metre bridge works on the principle of:
   a) Potentiometer
   b) Kirchhoff's Laws
   c) Wheatstone Bridge
   d) Ohm's Law

3. To minimize error in a metre bridge experiment, the balance point should ideally be obtained near:
   a) 0 cm
   b) 100 cm
   c) 50 cm
   d) Any point is equally accurate

4. In the experiment to find the internal resistance of a cell using a potentiometer, let l₁ be the balancing length with the cell in open circuit and l₂ be the balancing length when a resistance R is connected across the cell. The internal resistance 'r' is given by:
   a) r = R (l₁ / l₂)
   b) r = R (l₂ / l₁)
   c) r = R ( (l₁ - l₂) / l₂ )
   d) r = R ( (l₂ - l₁) / l₁ )

5. The sensitivity of a potentiometer can be increased by:
   a) Increasing the current in the main circuit
   b) Decreasing the length of the potentiometer wire
   c) Decreasing the potential gradient (k) along the wire
   d) Using a driver cell of lower EMF

6. In the half-deflection method for finding galvanometer resistance G, a shunt S is used to reduce deflection to half. The condition R >> G (where R is the series resistance) leads to the approximation:
   a) G ≈ R
   b) G ≈ S
   c) G ≈ R - S
   d) G ≈ R + S

7. To convert a galvanometer into an ammeter, one needs to connect:
   a) A high resistance in series
   b) A low resistance in series
   c) A high resistance in parallel (shunt)
   d) A low resistance in parallel (shunt)

8. Why should the key be inserted only while taking readings in the Ohm's law experiment?
   a) To save battery power
   b) To prevent heating of the resistance wire
   c) To protect the ammeter
   d) To protect the voltmeter

9. End corrections in a metre bridge experiment arise due to:
   a) Non-uniformity of the metre bridge wire
   b) Resistance of the copper strips and soldering points
   c) Heating of the wire
   d) Sliding the jockey instead of pressing it

10. The figure of merit of a galvanometer (k) is defined as:
    a) Voltage required for unit deflection
    b) Resistance required for unit deflection
    c) Current required for unit deflection
    d) Total deflection for unit current

Answers to MCQs:

1. b) Resistance
2. c) Wheatstone Bridge
3. c) 50 cm
4. c) r = R ( (l₁ - l₂) / l₂ )
5. c) Decreasing the potential gradient (k) along the wire
6. b) G ≈ S
7. d) A low resistance in parallel (shunt)
8. b) To prevent heating of the resistance wire
9. b) Resistance of the copper strips and soldering points
10. c) Current required for unit deflection

Study these notes thoroughly, focusing on the underlying principles and potential pitfalls in each experiment. Good luck with your preparation!