Final answer:
To calculate the energy cost per minute of operation for a DC generator, one can determine the electrical power output from the current and voltage and then calculate the total energy output over one minute. Subtracting this from the mechanical energy input per minute gives the energy cost per minute.
Step-by-step explanation:
The question involves calculating the energy cost per minute of operation for a DC generator. Given that mechanical energy is supplied at the rate of 4200 J/s and the generator delivers an electrical output of 32.2 A at 120 V, we need to find the electrical energy delivered and then the cost of energy per minute.
Firstly, electrical power output (P) can be calculated using the formula P = IV, where I is the current and V is the voltage. Substituting the given values, P = 32.2 A × 120 V = 3864 W or J/s.
Next, to find the energy delivered per minute, we multiply this power by 60 seconds (since there are 60 seconds in a minute), resulting in an energy output of 3864 J/s × 60 s = 231,840 J or 231.84 kJ per minute. Finally, the energy cost per minute is simply the mechanical energy input minus the electrical energy output over one minute. This results in an energy cost of (4200 J/s × 60 s) - 231,840 J, which needs to be calculated to get the final answer.