Question

The series combination of two batteries, both of the same emf 10 V, but different internal resistance of 20 Ω and 5 Ω, is connected to the parallel combination of two resistors 30 Ω and R Ω. The voltage difference across the battery of internal resistance 20 Ω is zero, the value of R (in Ω) is : _______

Answer 1

E₁ = E - ir

E₂ = E – ir

= 10 – i20 = 0

= 10 – 0.5 × 5

i = 0.5 A

= 7.5 V

E_net = E₁ + E₂ = 7.5 V

i = i₁ + i₂ 

0.5 = (7.5/x) + (7.5/30)

x = 30 Ω

Answer 2

x = (7.5/0.25) = 30