Which formula correctly expresses heat energy q in Joule's Law?

Which formula correctly expresses heat energy q in Joule's Law?

• A. q = V x I x t
• B. q = I^2 x R x t
• C. q = E x I x t
• D. q = I x R x t

Answer: (B)

Joule's Law ties heat produced in a resistor to the current through it, its resistance, and the time the current flows. The heat energy generated is the power dissipated as heat times time. In a resistor, the power is P = I^2 R, because the energy converted to heat per unit time grows with the square of the current and with the resistance. Multiplying by time gives the total heat: q = I^2 R t. This form directly uses the quantities involved (current, resistance, time) and yields units of joules correctly, since I^2 R t = A^2 × Ω × s = A × V × s = J.

Joule's Law ties heat produced in a resistor to the current through it, its resistance, and the time the current flows. The heat energy generated is the power dissipated as heat times time. In a resistor, the power is P = I^2 R, because the energy converted to heat per unit time grows with the square of the current and with the resistance. Multiplying by time gives the total heat: q = I^2 R t. This form directly uses the quantities involved (current, resistance, time) and yields units of joules correctly, since I^2 R t = A^2 × Ω × s = A × V × s = J.