Three parallel branches, each containing a cell and an internal resistance, are connected across a variable external load resistor R . The first branch contains a 20 V cell with 2 internal resistance, the second branch contains a 10 V cell with 2 internal resistance, and the third branch contains a 5 V cell with 1 internal resistance. All cells are connected with the same polarity. The value of the external resistor

Step-by-step solution

The equivalent internal resistance r_ eq of the three parallel branches is given by: 1 r_ eq = 1 r₁ + 1 r₂ + 1 r₃ = 1 2 + 1 2 + 1 1 = 2 ⁻¹ r_ eq = 0.5 The equivalent EMF E_ eq of the parallel combination is given by Millman's theorem: E_ eq = E₁ r₁ + E₂ r₂ + E₃ r₃ 1 r_ eq = ( 20 2 + 10 2 + 5 1 ) 0.5 E_ eq = (10 + 5 + 5) 0.5 = 20 0.5 = 10 V According to the Maximum Power Transfer theorem, the power dissipated in the external load R is maximum when R = r_ eq . Therefore, R = 0.5 . The maximum power is given by: P_ ma