My physics textbook states the following about a single loop circuit with a resistor and ideal battery. "From the principle of conservation of energy, the work done by the (ideal) battery must equal the thermal energy that appears in the resistor" Can anyone explain why energy must be conserved? Isn't the battery producing an applied force on the charges? How can we be sure this applied force is a conservative force? Also even if energy is conserved, why must the thermal dissipation equal the work done by the battery?