Final answer:
At the initial moment when the circuit is completed, the battery supplies power at a rate of 2.00 Watts, calculated by the formula P = V^2 / R with the provided values of voltage and resistance.
Step-by-step explanation:
Just after the circuit with the inductor and resistor is completed, the battery begins supplying electrical energy to the circuit. The rate at which energy is supplied, also known as power, can be calculated using the formula P = V^2 / R, where V is the voltage of the battery, and R is the total resistance in the circuit. Initially, since the inductor acts as a short circuit, the entire voltage appears across the resistor.
The initial power supplied by the battery to the circuit is therefore 4.00 V^2 / 8.00 Ω = 2.00 W. As the inductor's magnetic field builds, energy is also stored in the inductor with a rate of change given by dI/dt, which changes over time. However, since the question asks for the initial rate, the resistive dissipation is the primary consideration.