An infinite combination of resistors, each having resistance R = 4 Ω, is given below. What is the net resistance between the points A and B? (Each resistance is of equal value, R = 4)

This problem involves an infinite ladder network of resistors. Let the total equivalent resistance between points A and B be X. Because the network is infinite, the resistance of the circuit remains X even after removing the first repeating unit.

The simplified circuit consists of one series resistor R connected to a parallel combination of another resistor R and the equivalent resistance X. The governing equation is:
X = R + (R × X) / (R + X)

Substituting R = 4 Ω:
X = 4 + 4X / (4 + X)
X(4 + X) = 4(4 + X) + 4X
4X + X² = 16 + 4X + 4X
X² - 4X - 16 = 0

Using the quadratic formula [x = (-b ± √(b² - 4ac)) / 2a]:
X = [4 ± √(16 - 4(1)(-16))] / 2
X = (4 ± √80) / 2 = (4 ± 4√5) / 2 = 2 ± 2√5

Since resistance cannot be negative, the net resistance is 2 + 2√5 Ω, which matches Option B.