The problem of calculating power in a parallel RL circuit is a classic that has been dealt with for many years. It is an NP-hard problem and can be stated as
The voltage across each branch of a parallel RL circuit is the same value, equal in value to the total applied voltage, ET, and in phase with each other. This means that the overall voltage across the entire circuit is equal. The total current in a parallel RL circuit is equal to the vector sum of the branch currents because the branch currents are out of phase with each other. It can also be shown that the total current in a parallel RL circuit is equal to the sum of all branches currents, which includes all branch currents coming from one or more sources.