Question 20 of 31intermediate🔧 ApplyNumerical5 marks

The values of current I flowing in a given resistor for the corresponding values of potential difference V across the resistor are given below – I(amperes) 0.5 1.0 2.0 3.0 4.0 V(volts) 1.6 3.4 6.7 10.2 13.2 Plot a graph between V and I and calculate the resistance of that resistor.

Correct Answer

The resistance of the resistor is approximately 3.3 Ω.

Exercise: EXERCISES | Q: 7 | (Page Page 23)
For More Understanding

Explanation

According to Ohm's law from the textbook, V ∝ I, which means V/I = constant = R. The V-I graph is a straight line passing through the origin. To find resistance, we calculate V/I for each reading and take the average, or determine the slope of the V-I graph.

Solution Steps

  1. Step 1: According to Ohm's law, V = IR, therefore R = V/I. We calculate resistance for each pair of values.

  2. Step 2: R₁ = V₁/I₁ = 1.6/0.5 = 3.2 Ω

  3. Step 3: R₂ = V₂/I₂ = 3.4/1.0 = 3.4 Ω

  4. Step 4: R₃ = V₃/I₃ = 6.7/2.0 = 3.35 Ω

  5. Step 5: R₄ = V₄/I₄ = 10.2/3.0 = 3.4 Ω

  6. Step 6: R₅ = V₅/I₅ = 13.2/4.0 = 3.3 Ω

  7. Step 7: Average resistance R = (3.2 + 3.4 + 3.35 + 3.4 + 3.3)/5 = 16.65/5 = 3.33 Ω ≈\approx 3.3 Ω

  8. Step 8: Alternatively, using slope method: R = ΔV/ΔI = (13.2 - 1.6)/(4.0 - 0.5) = 11.6/3.5 = 3.31 Ω ≈\approx 3.3 Ω

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