A current of 16 amperes divides between two branches in parallel of resistances 8 ohms and 12 ohms . The current in each branch is:

Explanation

To calculate the current in each branch, we first need to calculate the total resistance of the circuit. The formula for the total resistance of two resistors in parallel is: 1/Rtotal = 1/R1 + 1/R2 where R1 and R2 are the resistances of the two branches. Plugging in the values, we get: 1/Rtotal = 1/8 ohm + 1/12 ohm 1/Rtotal = 5/24 ohm Rtotal = 24/5 ohm Now that we know the total resistance of the circuit, we can use Ohm's Law to calculate the voltage across the branches: V = I x Rtotal V = 16 A x 24/5 ohm V = 76.8 V Now we can use the formula I = V/R to calculate the current in each branch: For the 8-ohm branch: I = V / R I = 76.8 V / 8 ohm I = 9.6 A For the 12 ohm branch: I = V / R I = 76.8 V / 12 ohm I = 6.4 A Therefore, the current in the 8-ohm branch is 9.6 amperes, and the current in the 12-ohm branch is 6.4 amperes.