Which formula expresses power as P = I^2 × R?

Which formula expresses power as P = I^2 × R?

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

Answer: (A)

Power in a resistor is the rate at which electrical energy is converted to heat, which is given by P = VI. For a resistor, the voltage across it and the current through it are related by Ohm’s law V = IR. Substituting this into P = VI gives P = I × (IR) = I^2 R. This shows why power is proportional to the square of the current and to the resistance: if you double the current through the same resistor, the power turned into heat quadruples, and if you raise the resistance while keeping the current the same, more power is dissipated as heat as well. This form is particularly handy when you know the current and the resistance but not the voltage. The expression P = VI is the general power rule, and with Ohm’s law you can derive the other equivalent forms, such as P = V^2 / R, since V = IR implies V^2 / R = (IR)^2 / R = I^2 R. The option P = R / I wouldn’t yield the correct units for power, so it isn’t valid.

Power in a resistor is the rate at which electrical energy is converted to heat, which is given by P = VI. For a resistor, the voltage across it and the current through it are related by Ohm’s law V = IR. Substituting this into P = VI gives P = I × (IR) = I^2 R. This shows why power is proportional to the square of the current and to the resistance: if you double the current through the same resistor, the power turned into heat quadruples, and if you raise the resistance while keeping the current the same, more power is dissipated as heat as well.

This form is particularly handy when you know the current and the resistance but not the voltage. The expression P = VI is the general power rule, and with Ohm’s law you can derive the other equivalent forms, such as P = V^2 / R, since V = IR implies V^2 / R = (IR)^2 / R = I^2 R. The option P = R / I wouldn’t yield the correct units for power, so it isn’t valid.