​A student plots three graphs for I against V for three Ohmic conductors A, B and C. he found that the slope of these three graphs are 0.5, 0.1 and 0.2, respectively. If the conductors have the same length and their cross – section areas are in the ratio 1 : 2 : 3, then their resistivity rations i.e. ρ_A: ρδ: ρCwill be: ​

Correct option is C

The correct answer is (C) ​2 : 20 : 15​.

Understanding the Relationship

• Ohm's Law: For an Ohmic conductor, the relationship between current (I) and voltage (V) is linear, given by: V = IR where R is the resistance of the conductor.
• Slope of the Graph: In the I-V graph, the slope represents the reciprocal of the resistance (1/R).
• Resistivity (ρ): Resistivity is an intrinsic property of a material, related to its resistance by: $$R = ρ(\frac{L}{A})$$​where L is the length and A is the cross-sectional area.

Given Information:

• Slopes of the graphs: 0.5, 0.1, and 0.2
• Cross-sectional areas: 1:2:3
• Length: Same for all conductors

Calculations:

Calculate Resistance:

$$Resistance of A:\frac{1}{0.5}=2$$​

$$Resistance of B: \frac{1}{0.1}=10$$​

$$Resistance of C:\frac{1}{0.2}=5$$​

Calculate Resistivity:

Since the length is the same for all conductors, we can use the simplified formula:$$ρ={R}\times{A}$$​

$$Resistance of A: {2}\times{1}=2$$​

$$Resistance of B: {10}\times{2}={20}$$​

$$Resistance of C:{5}\times{3}=15$$​

Determine Resistivity Ratios:

$$ρA: ρB: ρC={2}:{20}:{15}$$​

​