An electrical power supply, such as a battery, generates an electrical potential (voltage, V) which varies depending on how much current (i) it is delivering. The integral represents the total power (energy per unit time) being given off by the battery when it is producing a current I. The useful electrical power, however, is just the product . The difference between the total and the electrical power represents power that is wasted (and that accumulates as heat). Consider a hypothetical battery with a voltage vs. current curve described by the equation . If the battery is producing a current of 4 amperes, how much electrical power is being produced, and how much power is being wasted?

Question

An electrical power supply, such as a battery, generates an electrical potential (voltage, V) which varies depending on how much current (i) it is delivering. The integral  represents the total power (energy per unit time) being given off by the battery when it is producing a current I. The useful electrical power, however, is just the product  . The difference between the total and the electrical power represents power that is wasted (and that accumulates as heat). Consider a hypothetical battery with a voltage vs. current curve described by the equation  . If the battery is producing a current of 4 amperes, how much electrical power is being produced, and how much power is being wasted?

Quizplus · Accepted Answer

The Answer of An electrical power supply, such as a battery, generates an electrical potential (voltage, V) which varies depending on how much current (i) it is delivering. The integral  represents the total power (energy per unit time) being given off by the battery when it is producing a current I. The useful electrical power, however, is just the product  . The difference between the total and the electrical power represents power that is wasted (and that accumulates as heat). Consider a hypothetical battery with a voltage vs. current curve described by the equation  . If the battery is producing a current of 4 amperes, how much electrical power is being produced, and how much power is being wasted?

An Electrical Power Supply, Such as a Battery, Generates an Electrical