An infinite ladder network is constructed using repeating L-sections. Each L-section consists of a series resistor of 1 and a parallel (shunt) resistor of 2 . This infinite network is connected across a battery of EMF 12 V and unknown internal resistance r . If the total steady current drawn from the battery is 4 A , the value of r is:

Step-by-step solution

Let the equivalent resistance of the infinite ladder network be R . Since adding one more L-section to an infinite ladder does not change its equivalent resistance, we can write: R = 1 + 2R 2 + R R(2 + R) = 2 + R + 2R 2R + R^2 = 3R + 2 R^2 - R - 2 = 0 (R - 2)(R + 1) = 0 Since resistance cannot be negative, R = 2 . The total resistance of the circuit is the sum of the ladder's equivalent resistance and the battery's internal resistance r . R_ total = R + r = 2 + r According to Ohm's law for the complete circuit: I =