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This problem involves two steps. First we need to figure out the amount of current in each light bulb. Then we use that value to find our two different resistances using Ohm's Law, and combine them to find our total resistance of the two bulbs.

For the first step, we need to know that the 30 and 40 watts they give us describe the light bulb's power, which is the rate at which they transform electricity into light and heat. There is an equation in physics which states that the power of a light bulb or other resistor (any object that takes up electricity in a circuit), is equal to its current, measured in amps, multiplied by the volts supplied by the battery. In equation form, P=IV, where P=power, I=current, and V=volts. We need I to find our resistance for the bulbs later.

The power of the first bulb is 30 watts, and the volts equals 120 V, so 30=I(120). I works out to be .25 amps for the first bulb. The second bulb has a power of 40 watts, but receives the same amount of volts as the first bulb because they are in the same circuit. So for the second bulb, 40=I(120), and I works out to be .333 amps.

Now because we have the resistances, we can use Ohm's Law for both bulbs. Ohm's Law states that the current equals the the voltage divided by the resistance, or I=(V/R). To make this easier, I'll change the equation a bit. We can multiply both sides by R to get IR=V, and then divide by I to get the new equation, R=V/I. This makes it easier for us to find our resistance directly with our values.

Then we simply plug in our I values which we found and the voltage of the battery to figure out the resistances. The first bulb's equation is R=120/.25, and the second bulb's equation is R=120/.333. Solving for the R's, the first bulb has a resistance of 360 Ohms, while the second bulb has a resistance of 480 Ohms.

If you just wanted the individual resistances, then those are your answers. But because you told me they were in series, it seems to me that you want their total resistance. We can find the total resistance for resistors in series by simply adding the resistances up. In this case, our total resistance would be 360 Ohms plus 480 Ohms, or 840 Ohms.

Take a look at the links below for more information. The first one explains the relationships between current, voltage, and resistance, and the second link discussed finding resistance in series and in parallel as well.

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Q: What is the resistance of two light bulbs in a series if one is 30watts and the other is 40watts with a 120volt battery?
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