Final answer:
The power delivered to a resistor with a known voltage across it can be calculated using the formula P = V²/R. This formula is derived from Ohm's law combined with the power relationship P = IV. Another expression for power is P = I²R, which is used when current and resistance are known.
Step-by-step explanation:
Power Delivered to a Resistor
The power P supplied to a resistor with resistance R when there is a voltage ΔV across it can be expressed using the formula: P = V²/R. This is derived from the combination of Ohm's law and the power formula P = IV, where I is the current. By substituting Ohm's law (V = IR) into the power equation, we get P = V²/R which represents power in terms of the voltage across the resistor and the resistance.
Another way to express power is by the formula P = I²R, where the current I is squared and multiplied by the resistance. This equation is obtained by rearranging Ohm's law to get I = V/R and then substituting I in the equation P = IV.
Both formulas P = V²/R and P = I²R are valid and depending on whether voltage or current is known alongside the resistance, either can be used to calculate the power delivered to a resistor. These formulas are crucial in understanding how power is related to voltage, current, and resistance in electrical circuits.