Which expression correctly represents the power dissipated by a resistor given current I and resistance R?

Which expression correctly represents the power dissipated by a resistor given current I and resistance R?

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

Answer: (A)

When a resistor carries current I and has resistance R, the power it dissipates as heat comes from P = VI, the voltage across the resistor times the current through it. For a resistor, Ohm’s law says V = IR, so substitute V with IR in P = VI to get P = I(IR) = I^2R. This directly ties the power to the given quantities I and R. Note that P = V^2 / R would also be valid, since substituting V = IR gives P = (IR)^2 / R = I^2R, but with the information provided (I and R), the straightforward form is P = I^2R. The other expressions don’t represent power using the specified I and R.

When a resistor carries current I and has resistance R, the power it dissipates as heat comes from P = VI, the voltage across the resistor times the current through it. For a resistor, Ohm’s law says V = IR, so substitute V with IR in P = VI to get P = I(IR) = I^2R. This directly ties the power to the given quantities I and R.

Note that P = V^2 / R would also be valid, since substituting V = IR gives P = (IR)^2 / R = I^2R, but with the information provided (I and R), the straightforward form is P = I^2R. The other expressions don’t represent power using the specified I and R.