Question

A load resistor

R Ω is fed by a parallel combination of two batteries. Battery A has an open ˚uit voltage of 46 V and an internal resistance of 7 Ω. Battery B has an open ˚uit voltage of 32 V and internal resistance of 4 Ω. Determine Thevenin's voltage (
V) that may be used to determine the power dissipated in the load resistor.

a) 25 V
b) 30 V
c) 35 V
d) 40 V

Answer 1

Thevenin's voltage (Vth) in this scenario is the voltage across the parallel batteries as seen from the load resistor, calculated using Vth = (VA/RA + VB/RB) / (1/RA + 1/RB), resulting in 40V.

Step-by-step explanation:

To determine Thevenin's voltage (Vth) for the load resistor which is fed by a parallel combination of two batteries, we need to find the voltage across the parallel combination as seen from the terminals of the load resistor. The total voltage can be found by transforming the circuit into its Thevenin equivalent, where the sources are replaced with a single voltage source and a single series resistance.

The Thevenin voltage Vth is the open-circuit voltage across the terminals when no load is connected, which in this case is equal to the voltage that would be measured across the parallel connection of the two batteries. Since we have a parallel circuit, we can use the formula for parallel voltage sources:

Vth = (VA/RA + VB/RB) / (1/RA + 1/RB)

Substituting the given values:

Vth = (46V/7Ω + 32V/4Ω) / (1/7Ω + 1/4Ω) = 40V

Therefore, the correct answer is 40V, which corresponds to option (d).