Power Rating of a Resistor. The power rating of a resistor is the maximum power the resistor can safely dissipate without too great a rise in temperature and hence damage to the resistor. (c) A 100.0-Ω and a 150.0-Ω resistor, both rated at 2.00 W, are connected in series across a variable potential difference. What is the greatest this potential difference can be without overheating either resistor, and what is the rate of heat generated in each resistor under these conditions?

Question

Accepted Answer

Hey everyone. So today we're dealing with a problem about circuits. So we're being told that the ability the ability of resistance to handle power is specified by a power rating. The maximum power a resistor can withstand without being damaged. So we're being told that two metal film resistors have a power rating of three watts And have resistance is R. one and r. two of 90 OEMs 140 homes respectively. With this we're being asked to determine two things. The greatest potential difference that can be used in the circuit as well as the rate of energy dissipation in each resistor. So let's tackle this one at a time. Let's start with the potential difference. In other words a potential difference is nothing but the voltage. Right? So we're being asked to find what is the greatest potential difference that can be used in the circuit. Well to do this we have the resistance is here. The total resistance is since they're connected in series, the total resistance is will simply be R. One plus R. Two Which is 90 homes plus 40 homes or a final answer of 230 homes. So that is the equivalent total resistance within the series system. We're being asked to find the greatest potential difference. This means we need to find what is the maximum current that we can get from this power rating of three. Why do we need current? Well that's because of OEMs Law, OEMs Law tells us the relation between voltage current and resistance. So to solve her voltage and we already have the total resistance is we need to solve recurrent but we don't have everything we need to solve recurrent yet at least not using OEMs Law. We need to use power as our guide. So we know that power we can recall. Power is equal to I squared R. However if we're going with the max power rating then this means we need to find the maximum current that flows through the resistor with the largest current. Or sorry, with the largest resistance With the 140 OMM resistance. So we know that the power is excuse me, we know that the power is three watts. So rearranging we can say that I max the maximum current is equal to is equal to the square root of P divided by The 140 Ohm resistor or are too right or are too me write rewrite that here as well or two Because it is the larger resistance Subsequuting in our values. We get the square root of three divided by 140 watts or 140 homes. Giving a final answer of 0.14639 Amps. So this is the maximum current which means plugging this into the OEMs Law. We know OEMs Law is equal to the current times the total total resistance. So substituting in our values, we get 0.14639 amps. Multiplied by 230 Ohms which gives us a voltage of 0.7 votes. So this is the maximum the greatest potential difference that can be used in the circuit. Now the rate of energy dissipation can also be done using this same power equation. Except now we're not using the or except now we're taking the current applied through the circuit because since we're in series the current applied to each resistor will be the same or it's the same throughout the system. But we're going to be using the individual resistance because we're trying to find the rate of energy anticipation in each resistor. So let's do that. So for a resistor 111 sequel to I squared R. One which is 0. 639 Amps multiplied by 90. OEMs Giving an answer of 1.93 watts. Excuse me. And we can do the same thing for resistor too. It's I squared multiplied by the resistance. Ah uh resistor too. And we already saw this earlier. If we rewrite this equation that we did right here. Since we said that the power rating was three when the amperage was 1.4639. And the resistance of 1 40 1 40. If we rewrite that out amps multiplied by 1:40 a.m. We get a power or energy dissipation of three watts. So the greatest potential difference that can be used in the circuit is 33.7V leaving us with answer choices B&C. And for the 90 Ohm resistor, the energy dissipated is 1.93 watts. and for the 140 Ohm resistor it is three watts, which leaves us with answer choice B. I hope this helps, and I look forward to seeing you all in the next one.

Verified Solution

Key Concepts

Ohm's Law

Power Dissipation in Resistors

Series Circuits