A typical small flashlight contains two batteries, each having an emf of 1.5 V, connected in series with a bulb having resistance 17 Ω. ((b) If the batteries last for 5.0 h, what is the total energy delivered to the bulb?

Video transcript

Hey, everyone in this problem, an electrical device runs using power supplied by 2 12 volt batteries connected in series. The resistance of the device is measured to be 5.4 ohms. If the device is used for one day, determine the total energy it takes from the batteries. Alright, so we're looking for total energy. Let's recall that the energy E is going to be equal to the power P times A times T. Now, in this problem, we are given the time t we know that the time T is going to be one day. Okay. Let's convert this to our standard unit of seconds. So we're gonna multiply one day by hours per day, the unit of day will cancel our left with ours. Then we can multiply 60 minutes, her one hour, the unit of our cancels, we're left with a unit of minutes and finally, we can multiply By 60 seconds per one minute. The unit of minute cancels and we're left with the unit of seconds, which is what we want. So we have one times 24 times 60 times 60. This is going to give us 86,000 400 seconds. Okay. So we have our time T now we also need the power P in order to calculate the total energy you were looking for. We're giving information about an electrical circuit. Okay. So let's think about the power here and recall that the power is equal to the voltage V times the current. I now we aren't given information about the current I, but we are given information about the resistance are so we're called through OEMs Law. We can relate the I and our, we know that I is going to be equal to V over R and so we can write the power as V squared over our. Now, when we're talking about the voltage here, we have two batteries and they're connected in series. Okay. So we want to consider the equivalent voltage for both of these. Now what's the equivalent voltage? Well, if we're in series, the equivalent voltage is going to just be the sum of the voltages. We have B one plus B two. In this case, both of our batteries are 12 old. And so we just have 12V Plus 12V which gives us 24 volts. Alright, so getting back to our power equation, we have the power is now equal to This equivalent voltage 24V squared divided by the resistance R. And we're told in the problem That the resistance is five 0. arms. Okay. So we're gonna divide By 5.4 24 volts squared divided by 5.4 OEMs gives us a value of 106. watts. Alright, so that's our power p. Remember we're looking for the energy and we wrote that the energy is equal to the power times of time we had the time we just needed to convert the units. Now we have the power so we can find our energy by multiplying the two together. So the energy is going to be equal to power times time. This is 106.6, watts times a time of 86,400 seconds, Which gives us the energy 9.216 times 10 to the six jewels. Okay. We have one time second which gives us jewel and that is that total energy we're looking for. We go back up to our answer choices and we round to three significant digits. We see that our answer corresponds with answer choice a 9. times 10 to the six Jules. Thanks everyone for watching. I hope this video helped see you in the next one.