Science (086) — CBSE Class 10 board question

(i) Note: Since the actual circuit diagram values are not visible, a standard version commonly used in CBSE exams is assumed:
Battery = 6 V; Current through R1 = 1 A; Voltage across R1 = 2 V; Current through R2 = 0.5 A.

(I) Potential difference across R2:
V(R2) = Total voltage − Voltage across R1 = 6 − 2 = 4 V

(II) Value of R2:
Using Ohm's law: $R_2 = \dfrac{V_2}{I_2} = \dfrac{4}{0.5} = \mathbf{8\ \Omega}$

(III) Value of R1:
$R_1 = \dfrac{V_1}{I_1} = \dfrac{2}{1} = \mathbf{2\ \Omega}$

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(ii) Factors on which resistance depends and derivation:

Resistance of a conductor depends on:

1. Length (l): Resistance increases with length.
2. Area of cross-section (A): Resistance decreases as area increases.
3. Nature of material (resistivity).

Derivation:

From experiments:
$$R \propto l \quad \text{and} \quad R \propto \frac{1}{A}$$

Combining:
$$R \propto \frac{l}{A}$$
$$\boxed{R = \rho \frac{l}{A}}$$

where $\rho$ (rho) is the electrical resistivity of the material (SI unit: Ω m), a characteristic property of the material.

Source: Chapter 11 – Electricity, Section 11.5

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• For part (i), substitute the actual diagram values — the method (Ohm's law and Kirchhoff's voltage rule) stays the same.
• For part (ii), examiners expect: 3 factors named + both proportionality relations written + final formula with definition of ρ. Missing the definition of resistivity or its unit loses a mark.
• Write $R = \rho \frac{l}{A}$ clearly — this is the key derivation line.