बैटरी के आंतरिक प्रतिरोध को मापने के लिए विभवमापी का उपयोग किया जाता है। R = 10 Ω के लिए, संतुलन बिंदु ℓ = 500 cm पर पाया जाता है और R = l Ω के लिए संतुलन बिंदु ℓ = 400 cm पर देखा जाता है। बैटरी का आंतरिक प्रतिरोध लगभग है:

Concept:

The internal resistance of a battery can be measured using a potentiometer by comparing the potential drops across known resistances in an external circuit. The balance point of the potentiometer corresponds to the condition where the potential drop across the external resistor equals the potential drop across the potentiometer wire.

Equations used,

• The potential drop across the potentiometer wire:
  • Vpot = kl,
  • where:
  • Vpot is the potential difference across the potentiometer wire,
  • k is the potential gradient (volts per cm),
  • l is the length at the balance point.
• Emf and Internal Resistance:
  • The internal resistance r of the battery can be found using the relationship:
  • Vterm = E - I r
  • Where:
  • E is the emf of the battery,
  • Vterm is the terminal voltage across the external resistor,
  • I is the current through the circuit,
  • r is the internal resistance.

गणना:

माना विभव प्रवणता λ है,

∴ i × 10 = λ × 500 = ε - ir_s

⇒ 500 λ = ε - 50 λrs

साथ ही,

i' × 1 = λ × 400 = ε = i'rs

\(∴ 100\lambda = 350\lambda \ r_s \Rightarrow r_s = \frac{10}{35} \approx 0.3 \Omega \)

∴ सही उत्तर विकल्प (4) है।