When a resistor with resistance R is connected to a 1.50-V flashlight battery, the resistor consumes 0.0625 W of electrical power. (Throughout, assume that each battery has negligible internal resistance.) (a) What power does the resistor consume if it is connected to a 12.6-V car battery? Assume that R remains constant when the power consumption changes.

Video transcript

Hello, fellow physicists today were to solve the following practice problem together. Though, first off, let's read the problem and highlight all the key pieces of information that we need to use in order to solve this problem, an electric device of R resistance is connected to an ideal battery with a potential difference of 1.2 volts and consumes an electric power current of 0.0835 watts, determine the power current consumed by the device when it is connected to a different ideal battery with a charge of 12.0 volts assuming that R remains constant throughout the changes in the power current consumption. Ok. So our end goal is to determine the power current consumed by the device when it's connected to a different ideal battery. And we also need to assume that R remains constant throughout the changes in the power current consumption. Fantastic. So we're given some multiple choice answers. They're all in the same units of watts. Let's read them off to see what our final answer might be. A is 8.35 multiplied by 10 to the power of negative four B is 8.35 multiplied by 10 to the power of negative three C is 0.835 and D is 8.35 watts. OK. So first off, let us recall and use the equation for electric power, which states that electric power represented by P is equal to the potential difference, which is represented by V squared divided by a capital R which represents the resistance note that we are told that the resistance remains constant in both cases. So now let us solve for capital R which represents resistance. So let's solve for resistance. So rearranging our electric power equation to isolate and solve for R, we'll get that R is equal to V squared divided by P. And if R is the same in both cases, we can write that, let's say, and we can write that R one is equal to R two. Thus, we can state that V one square divided by P one is equal to V squared or V two squared divided by P squared. And let's also make a quick note here that V one is equal to 1.2 volts. V two is equal to 12.0 volts and P one is equal to 0.0835 watts. And we do not know what the value for P two is. So we need to solve for P two. So now we can rearrange. So let's call the equation for V one squared divided by P one equal to V two squared divided by P two. Let's call that equation one. So now we need to rearrange equation one to isolate and solve for P two. So let's do that. So P two is equal to P one multiplied by V two squared divided by V one squared. So doing a little simplifying, we can state that P one is multiplied by V two divided by V one all squared. At this stage, we can plug in all of our known variables. And so for our final answer, so let's do that. So our electric power value was 0.0835 watts multiplied by 12.0 volts divided by 1.2 volts all squared. So when we plug that into a calculator, we should get 8.35 watts. And let's box that in green because this is our final answer. We did it. So the power consumed by the device when connected to a different battery is 8.35 watts. So looking at our multiple choice answers, the correct answer has to be the letter D 8.35 watts. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.