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The practical involves measuring current and voltage across different resistors to calculate resistance using Ohm's Law.

Physics

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Step-by-step solution

10 steps

This practical is designed to help you understand Ohm's Law and how to determine resistance in different circuit configurations.

Overall Objective:
The experiment involves measuring current (I) and voltage (V) across different resistors or circuit setups to calculate their resistance (R) using Ohm's Law (V = IR). You'll then analyze this data graphically and solve a related problem.

Part 1

Determining R₁

  1. Setup: You'll connect a circuit with a resistor (let's call it R₁), an ammeter to measure current (I₁), and a voltmeter to measure voltage (V₁) across R₁.
  2. Data Collection: You'll take five sets of readings. For each set, you'll adjust the power supply to increase the current (I₁) flowing through R₁ and record the corresponding voltage (V₁) across it.
  3. Calculation: For each set of readings, you'll calculate the resistance R₁ using the formula: R₁ = V₁ / I₁ (in Ohms, Ω)
  4. Tabulation: Record all your I₁, V₁, and calculated R₁ values in the first table provided.

Part 2

Determining R₂

  1. Setup: You'll connect a different circuit (as shown in Fig. 3.2, which isn't provided, but implies a different resistor or a combination of resistors). Let's call the resistance of this setup R₂. You'll use an ammeter to measure current (I₂) and a voltmeter to measure voltage (V₂) across R₂.
  2. Data Collection: Similar to Part 1, you'll take multiple readings, increasing the current (I₂) and recording the corresponding voltage (V₂).
  3. Calculation: For each set of readings, you'll calculate the resistance R₂ using the formula: R₂ = V₂ / I₂ (in Ohms, Ω)
  4. Tabulation: Record all your I₂, V₂, and calculated R₂ values in the second table provided.

Now let's look at the questions:

Part a

**Graphing V vs I

You need to plot two graphs on the same graph page:

  1. Graph 1: Plot the voltage V₁ (y-axis) against the current I₁ (x-axis) using the data from Part 1.
  2. Graph 2: Plot the voltage V₂ (y-axis) against the current I₂ (x-axis) using the data from Part 2. Both graphs should ideally be straight lines passing through the origin, demonstrating Ohm's Law.

Part b· 6 steps

**Comparing Slopes and Average Resistances

  1. Calculate the average value of R₁ from your tabulated data in Part 1.

  2. Calculate the slope of the first graph (V₁ vs I₁).

    The slope of a V-I graph represents the resistance (ΔV/ΔI = R).

  3. Compare the calculated average R₁ with the slope of the first graph.

    They should be very close.

  4. Calculate the average value of R₂ from your tabulated data in Part 2.

  5. Calculate the slope of the second graph (V₂ vs I₂).

  6. Compare the calculated average R₂ with the slope of the second graph.

    They should also be very close.

Part c· 4 steps

**Calculating Resistor for Parallel Connection

You need to find the value of a resistor (let's call it Rₓ) that, when connected in parallel with a 2 Ω resistor, results in an effective resistance (R_eff) of 1.5 Ω.

  1. Write the formula for two resistors in parallel

    1/R_eff = 1/R₁ + 1/R₂

  2. Substitute the given values

    1/1.5 Ω = 1/Rₓ + 1/2 Ω

  3. Isolate 1/Rₓ

    1/Rₓ = 1/1.5 Ω - 1/2 Ω
    1/Rₓ = (2 - 1.5) / (1.5 × 2)
    1/Rₓ = 0.5 / 3
    1/Rₓ = 1/6

  4. Solve for Rₓ

    Rₓ = 6 Ω

    The value of the resistor to be connected in parallel is 6 Ω.

Part d

**Precautions for Accurate Results

Here are four precautions you could take:

  • Ensure all connections are tight and clean to minimize contact resistance.
  • Read the ammeter and voltmeter scales perpendicularly to avoid parallax error.
  • Use a rheostat or variable power supply to gradually change the current and voltage, taking readings at regular intervals.
  • Allow the circuit to cool down between readings or after prolonged use, as resistance can change with temperature.
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