Question:

A 12-V battery causes a current of 0.60 A through a resistor.

- What is its resistance, and
- how many joules of energy does the battery lose in a minute?

Source: Giancoli, Douglas C., Physics: Principles with Applications, 7th Edition, 2014.

Quick Answer:

- $20 \Omega$
- $430 \textrm{ J}$

### Transcript for this Giancoli solution

This is Giancoli Answers with Mr. Dychko. Knowing that voltage is current times resistance, we can divide both sides by*I*to solve for

*R*. So the resistance is the car battery voltage divided by the current. So that's 12 volts, divided by .6 amps, which is 20 ohms. And the current, we know, is charge passing a certain point, divided by time. And, we can solve this for

*Q*by multiplying both sides by

*t*and the charge, then, is gonna be the current multiplied by time. And the reason that's important is because the total energy that's lost in a minute, is gonna be the amount of charge that passes in a minute, multiplied by voltage. And because this is Joules per Coulomb -- that's what voltage is, it's the potential energy difference per Coulomb. So we multiply by Coulombs to get the actual energy difference,

*Delta PE*. And so, the number of Coulombs, then, is

*It*. And so, the current is .6 amps, and multiply it by one minute, times 60 seconds per minute, because we need our time to be in seconds, and multiply it by 12 volts, and we get 430 Joules of energy lost in one minute.