Which expression correctly gives energy delivered to a resistor with constant voltage V across it for time t?

Which expression correctly gives energy delivered to a resistor with constant voltage V across it for time t?

• A. E = V^2 / R × t
• B. E = V^2 R t
• C. E = V^2 t / R^2
• D. E = V^3 t / R

Answer: (A)

Energy delivered equals power times time. For a resistor with a steady voltage V across it, the current is I = V/R, so the power dissipated is P = VI = V*(V/R) = V^2/R. With that power constant, the energy over time t is E = P t = (V^2/R) t. This matches the chosen expression. The other forms would mix in wrong dependencies on V and R or yield incorrect units for energy.

Energy delivered equals power times time. For a resistor with a steady voltage V across it, the current is I = V/R, so the power dissipated is P = VI = V*(V/R) = V^2/R. With that power constant, the energy over time t is E = P t = (V^2/R) t. This matches the chosen expression. The other forms would mix in wrong dependencies on V and R or yield incorrect units for energy.