A flashlight uses two AA 1.5-V batteries connected in series t...

Question

A flashlight uses two AA 1.5-V batteries connected in series to provide 3.0 V across the bulb, as in Fig. 25–4b. The bulb draws 135 mA when turned on.

(a) Calculate the resistance of the bulb and the power dissipated.

(b) By what factor would the power increase if four AA batteries in series (total 6.0 V) were used with the same bulb? (Neglect heating effects of the filament.) Why shouldn’t you try this?

Accepted Answer

Hi, everyone. Let's take a look at this practice problem dealing with power in this problem. A desktop computers, internal fan operates at 12 volts and draws a current of 0.2 amps. This question has two parts for part one, calculate the resistance and power the fan. And for part two, if the voltage supply is tripled to 36 volts with the same fan, by what factor does the power increase? We give four possible choices as our answers or choice. A for part one, the resistance is 2.4 ohms and the power is 60 watts. And for part two, the power increases by a factor of nine. For choice B for part one, the resistance is 2.4 ohms. The power is equal to 60 watts. And for part two, the power increases by a factor of 27. For choice C for part one, the resistance is 60 ohms and the power is 2.4 watts. And for part two, the power increases by a factor of nine. And for choice D for part one, the resistance is 60 ohms and the power is equal to 2.4 watts and for part two, the power increases by a factor of 27. Now, for part one, we need to calculate two quantities, the resistance and the power of the fan. So we're actually gonna start off with the resistance. And for this, we're going to use Ohm's Law. So we call for Ohm's law that we have V is equal to I multiplied by R where V is the voltage I is the current and R is the resistance. We're asked to calculate the resistance. So I'll need to solve this for R by dividing both sides by I. And so we'll get R is equal to V divided by I. We have the voltage and the current given to us in the problem. So we can plug those values in. We'll have R is equal to where the voltage that is gonna be 12 volts that's gonna be divided by the current, which is 0.2 amps. And when I plug these values into my calculator, I'll get R is equal to 60 ohms. Recall that a volt divided by, gives you units of ohms. So that's gonna be the first half of the answer for part one. For the second half, we need to calculate the power for this. You need to recall your definition of power for a circuit and recall that, that uh formula is P is equal to I multiplied by V where P is the power I is the current envy is the voltage, we have both the current and the voltage given to us in the problem. So we can go ahead and plug in values. So we'll have P is equal to the current. I, that's gonna be 0.2 amps. That's gonna be multiplied by our voltage, which is 12 volts. That means that P is gonna be equal to 2.4 watts to recall that an amp multiplied by volt does give you units of watts. So that's gonna be your second half of our answer for part one. And so now I have the complete answer for part one since I have both parts done. Now, for part two, I need to calculate the factor by which the power increases if I've tripled the voltage of the power supply. And so I'm gonna be calculating the ratio of our new power, which we'll call P prime divided by our old power P. And what I want to do here is write our power in terms of the voltage and the resistance because the voltage is changing. However, since I'm using the same fan, the resistance is not changing, we can't use the P is equal to IV, since if I change the voltage that's also going to change the current by Ohm's law. So for this uh ratio is gonna be equal to, and for P prime, we're going to recall our formula for the power being dissipated by a resistor in terms of the voltage and the resistance, the fan is acting like a resistor. And so we call for that formula will have V prime squared divided by R. And that quantity is going to be divided by the quantity or P. We'll write that as V squared divided by R where V prime here is our new voltage V is our original voltage and R is the resistance of the fan. Now, the resistance R is going to cancel out. And I can also write our new voltage V prime in terms of our original voltage. Since we're told that the voltage supply um is tripled to 36 volts, that means that V prime is equal to three V. So I can plug um three VN four V prime. So when I do that, I'll get P prime divided by P, it's going to be equal to the quantity of three V and quantity squared divided by V squared. The V squared terms will cancel and I'll just be left with three squared, which is nine. So that means that P prime divided by P is going to be equal to nine. And that's the factor by which the power is increasing. So now if I look at my answer choices, the correct answer choice corresponds to answer choice. C So just a quick recap of what we've done here. Part one, we use Ohms law to calculate the resistance and we use our definition of power to calculate the power that's being used by the fan. For part two, we simply just took the ratio of our new power with respect to our old power. And we wrote the power in terms of the voltage and the resistance. We also made the um identification that our new voltage is just equal to three times our original voltage. So that allowed us to calculate our factor by which the power increased. So I hope that this has been useful and I'll see you in the next video.

Key Concepts

Ohm's Law

Power in Electrical Circuits

Series Circuits

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