CLASS 10 CBSE PHYSICS PRACTICAL

EXPERIMENT: Determination of the Equivalent Resistance of Two Resistors When Connected in Series and Parallel

AIM:

To determine the equivalent resistance of two resistors when connected in:

  1. Series combination
  2. Parallel combination

MATERIALS REQUIRED:

S. No.ApparatusRange/SpecificationQuantity
1Resistor R₁1Ω, 2Ω, or 5Ω1
2Resistor R₂1Ω, 2Ω, or 5Ω1
3Ammeter0-500mA or 0-1A1
4Voltmeter0-3V or 0-5V1
5Battery/Battery eliminator3V-6V1
6RheostatVariable resistance1
7Plug keyOne way1
8Connecting wires–As required
9Piece of sandpaper–1

THEORY:

Resistance: The property of a conductor that opposes the flow of electric current through it. It is measured in Ohms (Ω).

Ohm’s Law:

V = IR
Therefore, R = V/I

A. SERIES COMBINATION:

When resistors are connected end-to-end, they are said to be in series.

Properties:

  • The same current flows through each resistor
  • Total voltage = Sum of individual voltages (V = V₁ + V₂)
  • Equivalent resistance is the sum of individual resistances

Formula:

Rs = R₁ + R₂

Where:

  • Rs = Equivalent resistance in series
  • R₁, R₂ = Individual resistances

Note: Equivalent resistance in series is greater than the largest individual resistance.

B. PARALLEL COMBINATION:

When one end of all resistors is connected to one point and the other ends to another point, they are said to be in parallel.

Properties:

  • The voltage across each resistor is the same
  • Total current = Sum of individual currents (I = I₁ + I₂)
  • Reciprocal of equivalent resistance equals sum of reciprocals of individual resistances

Formula:

1/Rp = 1/R₁ + 1/R₂

Or, Rp = (R₁ × R₂)/(R₁ + R₂)

Where:

  • Rp = Equivalent resistance in parallel
  • R₁, R₂ = Individual resistances

Note: Equivalent resistance in parallel is less than the smallest individual resistance.

CIRCUIT DIAGRAMS:

A. Series Combination:

        ┌──[Rheostat]──[A]──[R₁]──[R₂]──┐
        │                                 │
     [+]Battery[-]                       │
        │                                 │
        └────────[Key]───────────────────┘
                      │
                     [V]
                      │
              (Across both resistors)

B. Parallel Combination:

        ┌──[Rheostat]──[A]──┬──[R₁]──┬──┐
        │                    │        │   │
     [+]Battery[-]           └──[R₂]──┘  │
        │                                 │
        └────────[Key]───────────────────┘
                      │
                     [V]
                      │
              (Across both resistors)

Legend:

  • A = Ammeter (in series)
  • V = Voltmeter (in parallel across the combination)
  • R₁, R₂ = Resistors
  • Key = Plug key

PROCEDURE:

PART A: SERIES COMBINATION

  1. Clean the ends of connecting wires with sandpaper.
  2. Connect the circuit as shown in the series circuit diagram.
  3. Connect resistors R₁ and R₂ in series (end-to-end).
  4. Connect ammeter in series with the combination.
  5. Connect voltmeter in parallel across both resistors (R₁ and R₂).
  6. Check all connections are tight and correct.
  7. Keep the rheostat at maximum resistance position.
  8. Insert the plug key to close the circuit.
  9. Adjust the rheostat to get a suitable reading on the ammeter.
  10. Note the ammeter reading (I) and voltmeter reading (V).
  11. Take at least 3 readings by changing the rheostat position.
  12. Record observations in the table.
  13. Calculate Rs using Rs = V/I for each observation.
  14. Find the mean value of Rs.

PART B: PARALLEL COMBINATION

  1. Disconnect the series circuit.
  2. Connect the circuit as shown in the parallel circuit diagram.
  3. Connect resistors R₁ and R₂ in parallel (both ends connected together).
  4. Connect ammeter in series with the combination.
  5. Connect voltmeter in parallel across both resistors.
  6. Check all connections are tight and correct.
  7. Keep the rheostat at maximum resistance position.
  8. Insert the plug key to close the circuit.
  9. Adjust the rheostat to get a suitable reading on the ammeter.
  10. Note the ammeter reading (I) and voltmeter reading (V).
  11. Take at least 3 readings by changing the rheostat position.
  12. Record observations in the table.
  13. Calculate Rp using Rp = V/I for each observation.
  14. Find the mean value of Rp.

OBSERVATIONS:

Given:

  • Resistance of first resistor, R₁ = _ Ω (e.g., 2Ω)
  • Resistance of second resistor, R₂ = _ Ω (e.g., 3Ω)

Least Count of Ammeter = _ A (e.g., 0.01 A)

Least Count of Voltmeter = _ V (e.g., 0.1 V)

OBSERVATION TABLES:

Table 1: SERIES COMBINATION

S. No.Current I (A)Potential Difference V (V)Equivalent Resistance Rs = V/I (Ω)
10.201.05.0
20.251.35.2
30.301.55.0

Mean Equivalent Resistance in Series:

Rs (mean) = (5.0 + 5.2 + 5.0) / 3 = 5.07 ≈ 5.1 Ω

Table 2: PARALLEL COMBINATION

S. No.Current I (A)Potential Difference V (V)Equivalent Resistance Rp = V/I (Ω)
10.600.71.17
20.700.81.14
30.800.91.13

Mean Equivalent Resistance in Parallel:

Rp (mean) = (1.17 + 1.14 + 1.13) / 3 = 1.15 ≈ 1.2 Ω

(Note: Above values are sample readings for R₁ = 2Ω and R₂ = 3Ω)

CALCULATIONS:

Given:

  • R₁ = 2Ω (example)
  • R₂ = 3Ω (example)

A. SERIES COMBINATION:

Theoretical Value:

Rs (theoretical) = R₁ + R₂
Rs = 2 + 3
Rs = 5 Ω

Experimental Value (from observations):

Rs (experimental) = 5.1 Ω

Verification: Experimental value ≈ Theoretical value ✓

B. PARALLEL COMBINATION:

Theoretical Value:

1/Rp = 1/R₁ + 1/R₂
1/Rp = 1/2 + 1/3
1/Rp = 3/6 + 2/6
1/Rp = 5/6
Rp = 6/5
Rp = 1.2 Ω

OR using the formula:
Rp = (R₁ × R₂)/(R₁ + R₂)
Rp = (2 × 3)/(2 + 3)
Rp = 6/5
Rp = 1.2 Ω

Experimental Value (from observations):

Rp (experimental) = 1.2 Ω

Verification: Experimental value ≈ Theoretical value ✓

RESULT:

For two resistors R₁ = 2Ω and R₂ = 3Ω:

  1. Series Combination:
  • Theoretical equivalent resistance: Rs = 5.0 Ω
  • Experimental equivalent resistance: Rs = 5.1 Ω
  • Verification: Rs > R₁ and Rs > R₂ ✓
  1. Parallel Combination:
  • Theoretical equivalent resistance: Rp = 1.2 Ω
  • Experimental equivalent resistance: Rp = 1.2 Ω
  • Verification: Rp < R₁ and Rp < R₂ ✓

Conclusion:

  • In series combination, equivalent resistance increases and is equal to the sum of individual resistances.
  • In parallel combination, equivalent resistance decreases and is less than the smallest individual resistance.

PRECAUTIONS:

General:

  1. Clean the ends of connecting wires with sandpaper before use.
  2. All connections should be neat, tight, and according to circuit diagram.
  3. Connect ammeter in series and voltmeter in parallel.
  4. Ensure positive terminals of ammeter and voltmeter are towards the positive terminal of the battery.

During Experiment:

  1. Check for zero error in ammeter and voltmeter before starting.
  2. Insert the plug key only while taking readings to avoid heating of resistors.
  3. Adjust the rheostat slowly and smoothly.
  4. Do not exceed the maximum current rating of the resistors.
  5. Take readings only when the meter needles are steady.
  6. Avoid parallax error – eye should be perpendicular to the scale while reading.

Safety:

  1. Do not touch the circuit while it is ON.
  2. Switch off immediately if any component gets overheated.
  3. Use appropriate range instruments to avoid damage.
  4. Take at least 3 readings for accuracy.

Circuit Specific:

  1. In series combination, ensure resistors are connected end-to-end.
  2. In parallel combination, ensure both ends of resistors are connected to common points.
  3. Double-check connections before closing the key.
  4. Note the polarity of meters carefully.

SOURCES OF ERROR:

  1. Loose connections in the circuit
  2. Zero error in instruments not accounted for
  3. Heating effect due to prolonged current flow
  4. Incorrect connections (series/parallel)
  5. Parallax error while reading meters
  6. Internal resistance of battery not negligible
  7. Resistance of connecting wires not negligible

VIVA QUESTIONS:

1. Q: What is the formula for equivalent resistance in series?

  • A: Rs = R₁ + R₂ + R₃ + …

2. Q: What is the formula for equivalent resistance in parallel?

  • A: 1/Rp = 1/R₁ + 1/R₂ + 1/R₃ + …

3. Q: Which combination gives higher resistance – series or parallel?

  • A: Series combination gives higher resistance.

4. Q: Why is equivalent resistance in parallel less than individual resistances?

  • A: Because in parallel, multiple paths are available for current flow, reducing overall resistance.

5. Q: If two equal resistors of 4Ω each are connected in series, what is the equivalent resistance?

  • A: Rs = 4 + 4 = 8Ω

6. Q: If two equal resistors of 4Ω each are connected in parallel, what is the equivalent resistance?

  • A: Rp = (4 × 4)/(4 + 4) = 16/8 = 2Ω

7. Q: Why is ammeter connected in series?

  • A: To measure the total current flowing through the circuit.

8. Q: Why is voltmeter connected in parallel?

  • A: To measure the potential difference across the resistor combination.

9. Q: What happens to total resistance when more resistors are added in series?

  • A: Total resistance increases.

10. Q: What happens to total resistance when more resistors are added in parallel?

  • A: Total resistance decreases.

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