Question

The potential difference between the terminals of a battery is 10V and internal resistance 1Ω drops to 8V when connected across an external resistor find the resistance of the external resistor.

(A) 40 Ω

(B) 0.4 Ω

(C) 4M Ω

(D) 4 Ω

Answer 1

The correct option (D) 4 Ω

Explanation:

initially P.d = 10V with r = 1Ω

when R is connected p.d = 8V

∴ (V'/I) = r parallel with R

∴ (V'/I) = {(r ∙ R)/(r + R)} = {(1 × R)/(1 + R) = {R/(R + 1)}

Also initially V = Ir hence I = (V/r) = (10/1) = 10A

∴ (V'/I) = (8/10) = {R/(R + 1)}

∴ 8R + 8 = 10R

∴ R = 4Ω