The rate at which energy is delivered by an electric current is determined by the power of the circuit. Power (P) in an electrical circuit is the rate at which energy is transferred or the rate at which work is done. The mathematical relationship between power, current, voltage, and resistance is given by Ohm’s Law and the power formula.

Power Formula:

P = I . V

where:

» P is the power (in watts),
» I is the current (in amperes),
» V is the voltage (in volts).

Alternative Power Formula (using Ohm’s Law):

P = I² . R
P = V²/R

Where:

» R is the resistance (in ohms).
Factors Determining Power and Energy Delivery Rate:

1. Current (I): The higher the current flowing through a circuit, the higher the power. Current represents the flow of electric charge, and the rate of this flow contributes to the overall power.

2. Voltage (V): The voltage across the circuit is a critical factor. Higher voltage means more electrical potential energy per unit charge, and this results in higher power.

3. Resistance (R): Resistance affects power through the relationship P=I² ⋅R and P= V²/R.

​Higher resistance leads to higher power dissipation for a given current and voltage.

4. Combination of Resistance and Voltage (Ohm’s Law): The combination of resistance and voltage, as described by Ohm’s Law (V = I⋅R), influences the power delivered to a circuit.

In summary, the rate at which energy is delivered in an electric circuit, or the power, is determined by the interplay of current, voltage, and resistance. Controlling any of these factors can affect the power consumption or delivery in an electrical system.