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NEET2026PhysicsChapterActual

A uniform resistance wire MN of total resistance R₀ is connected across an ideal DC voltage source. A load resistor R_L is connected between the end M and a sliding contact S on the wire. If the sliding contact is positioned such that the length MS is two-thirds of the total length of the wire MN , what is the ratio of the potential difference across the load resistor R_L to the potential difference across the remain

Options

  1. A6 R_L 2 R₀ + 3 R_L
  2. B3 R_L 2 R₀ + 6 R_L
  3. C2 R₀ + 3 R_L 6 R_L
  4. D2 R_L 3 R₀ + 2 R_L

Correct answer

A. 6 R_L 2 R₀ + 3 R_L

Step-by-step solution

Let the total resistance of the wire MN be R₀ . Since the wire is uniform and the length MS is two-thirds of the total length MN , the resistance of the segment MS is: R_ MS = 2 3 R₀ The resistance of the remaining segment SN is: R_ SN = R₀ - 2 3 R₀ = 1 3 R₀ The load resistor R_L is connected in parallel with the segment MS . The equivalent resistance R_ eq1 of this parallel combination is: R_ eq1 = R_L R_ MS R_L + R_ MS = R_L ( 2 3 R₀ ) R_L + 2 3 R₀ = 2 R_L R₀ 3 R_L + 2 R₀ The segment SN is in series with this par

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