Question

Two resistances of 6 ohms and 8 ohms are connected in parallel. This combination is connected in series to another parallel combination of 2 ohms and 5 ohms. If the current in the whole combination is 15 amperes, determine the voltage in each resistor.

Answer 1

the combined resistance of two in parallel is ... product / sum

resistors in parallel have the same voltage drop

the 6/8 combo ... (6 * 8) / (6 + 8) = 48 / 14 = 24 / 7
... voltage = 15 * 24/7

the 5/2 combo ... (5 * 2) / (5 + 2) = 10 / 7
... voltage = 15 * 10/7

Answer 2

The circuit is equivalent to two resistors R1 and R2 in series, where
1/R1 = 1/6 + 1/3
1/R2 = 1/2 + 1/5
So the whole setup has a resistance of R = R1+R2 = 24/7 ohms
That means the voltage across it all is V = 15 * 24/7 = 360/7 volts
That means that the voltage across the pairs of parallel resistors is
V1 = R1/R * V
V2 = R2/R * V
Now finish it off by using the 15A current across each resistor pair to get the voltage drop on each resistor.