Question

If the resistance of a conductor is doubled while keeping the potential difference across its ends constant, what will happen to the current flowing through it?

• A. It will double
• B. It will halve
• C. It will remain unchanged.
• D. It will quadruple

Answer 1

Answer:

B. It will halve

Ohm's Law Relationship

• According to Ohm's Law, the electric current (I) flowing through a conductor is directly proportional to the potential difference (V) applied across its ends and inversely proportional to its resistance (R).
• The mathematical formula for Ohm's Law is: V = I × R or I = V / R.

Impact of Doubling Resistance

• From the equation I = V / R, current is inversely proportional to resistance (I ∝ 1/R) when voltage remains constant.
• If the resistance is doubled (R' = 2R), the new current becomes I' = V / (2R) = I / 2.
• Therefore, doubling the resistance causes the current to become half of its original value.

Key Factors Affecting Resistance

• Length (l): Resistance is directly proportional to the length of the conductor (R ∝ l). Doubling the length doubles the resistance.
• Cross-sectional Area (A): Resistance is inversely proportional to the area of cross-section (R ∝ 1/A). Doubling the thickness/area halves the resistance.
• Resistivity (ρ): Resistance depends on the nature of the material, given by the formula R = ρ × (l / A).
• Temperature: For metallic conductors, resistance increases as temperature increases.