Which equation correctly expresses power using voltage and resistance only?

Which equation correctly expresses power using voltage and resistance only?

• A. P = V^2 / R
• B. P = V × I
• C. P = I^2 × R
• D. P = V × R

Answer: (A)

Power is the rate at which energy is transferred, and for an electrical circuit it’s given by P = VI. When you only know the voltage across a resistor and its resistance, you can replace the current using Ohm’s law: I = V/R. Substituting this into P = VI gives P = V × (V/R) = V^2/R. This form uses just voltage and resistance and yields the correct unit for power, watts, since volt squared divided by ohms simplifies to watts. The other ways to write power involve current explicitly (P = VI uses I) or mix voltage with resistance inappropriately (P = V × R isn’t a valid expression for electrical power). The V^2/R expression is the correct way to express power using voltage and resistance only.

Power is the rate at which energy is transferred, and for an electrical circuit it’s given by P = VI. When you only know the voltage across a resistor and its resistance, you can replace the current using Ohm’s law: I = V/R. Substituting this into P = VI gives P = V × (V/R) = V^2/R. This form uses just voltage and resistance and yields the correct unit for power, watts, since volt squared divided by ohms simplifies to watts.

The other ways to write power involve current explicitly (P = VI uses I) or mix voltage with resistance inappropriately (P = V × R isn’t a valid expression for electrical power). The V^2/R expression is the correct way to express power using voltage and resistance only.