a 12V , 3A motor takes 120 minutes to do a certain job. a 120V, 8A motor takes 5 minutes to do the same job. Which motor uses the least energy and by how much?

energy=voltage*current*timeinseconds

where energy is in Joules.

a)


Power of the motor P = 3.8hp
= (3.8hp)(746W/hp)
= 2834.8W
Motor is 90% efficient.
Therefore Power absorbed by the motor is (2834.8W)/(0.9) =3150W
But power P = V I
then current in the motor I =(3150W)/(120V)
= 26.25A

(b)
Energy delivered to the motor E = P*t
= (3150W)(4h)(3600s/h)
= 4.536 *107J

(c) E = (3150W)(4h)
=(3.15*4)kWh
=12.6kWh
Therefore cost to run the motor for 4h is(12.6kWh)($0.16/kWh)
= $2.016

To determine which motor uses the least energy, we need to calculate the amount of energy used by each motor. Energy is calculated by multiplying the power rating of the motor by the time it takes to perform the job.

Let's start with the first motor that has a power rating of 12V and 3A and takes 120 minutes to do the job. The power (P) of a motor can be calculated using the formula P = V * I, where V is the voltage and I is the current. So, the power of the first motor is P1 = 12V * 3A = 36W.

Now, let's calculate the energy (E1) used by the first motor using the formula E = P * t, where t is the time taken to perform the job. So, E1 = 36W * 120 minutes = 4320 watt-minutes.

Moving on to the second motor with a power rating of 120V and 8A, which takes 5 minutes to complete the same job. The power (P2) of the second motor is P2 = 120V * 8A = 960W.

Now, let's calculate the energy (E2) used by the second motor using the same formula as before. E2 = 960W * 5 minutes = 4800 watt-minutes.

Comparing the results, we find that the first motor (12V, 3A) uses 4320 watt-minutes of energy, while the second motor (120V, 8A) uses 4800 watt-minutes of energy.

Therefore, the first motor uses the least energy by 4800 - 4320 = 480 watt-minutes.