In the circuit above the ammeter reads a curren... - JAMB Physics 1999 Question

In the circuit above, the ammeter reads a current of 5.0 A when R = 8Ω and reads 7.0A when R = 5Ω. The value of the unknown resistance X is

From Ohms Law, E = I(R +X)

=> E = I₁(R₁ + X)

again, E = I₂(R₂ + X)

=> I₁(R₁ + X) = I₂(R₂ + X)

∴ 5(8 + X) = 7(5 + X)

40 + 5X = 35 + 7X

7X - 5X = 40 - 35

2X = 5

X = ⁵/₂

= 2.5Ω