TBR Electric Circuits question

[cloak25]

For two cylindrical resistors made of identical material and with equal radii, R1 and R2, where R1 is longer than R2, what is true when the two are in parallel?

A) R1 dissipates more heat than R2
B) R2 dissipates more heat than R1
C) R1 experiences a greater voltage drop than R2
D) R2 experiences a greater voltage drop than R1

In the passage, it states that "if two resistors experience the same current, then the one with greatest resistance dissipates the most heat."

So wouldn't the answer be A? according to the formula given by TBR R= rho (L/A) where L = length, R = resistance, A = area and rho = resistivity of material. (the real answer is actually B).

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[MedPR]

For two cylindrical resistors made of identical material and with equal radii, R1 and R2, where R1 is longer than R2, what is true when the two are in parallel?

A) R1 dissipates more heat than R2
B) R2 dissipates more heat than R1
C) R1 experiences a greater voltage drop than R2
D) R2 experiences a greater voltage drop than R1

In the passage, it states that "if two resistors experience the same current, then the one with greatest resistance dissipates the most heat."

So wouldn't the answer be A? according to the formula given by TBR R= rho (L/A) where L = length, R = resistance, A = area and rho = resistivity of material. (the real answer is actually B).

I'm confused by the question. It says equal radii, then it says Radius1>Radius2.

However, if Radius1>Radius2, then Area1>Area2. Resistance and area are inversely proportional. So the one with the bigger area has the smaller resistance, P=Also, two resistors in parallel don't experience the same current, they experience the same voltage drop.

V=IR
I=V/R
P=I^2R
P=V^2/R

Bigger A = smaller resistance
Same V, smaller resistance = bigger Power. So P2 > P1.

 

[SaintJude]

This a typical TBR questions. The concepts they focus on are great, but this question is flawed.

The formula given for intrinsic resistance, shows that resistance is proportional to length. So R1 > R2.

"if two resistors experience the same current, then the one with greatest resistance dissipates the most heat."

Then that should be indeed A.

What does the explanation say.

 

[MedPR]

This a typical TBR questions. The concepts they focus on are great, but this question is flawed.

The formula given for intrinsic resistance, shows that resistance is proportional to length. So R1 > R2.

"if two resistors experience the same current, then the one with greatest resistance dissipates the most heat."

Then that should be indeed A.

What does the explanation say.

But the question asks about two resistors in parallel, so they will experience the same voltage drop and different currents.

Where did I go wrong in my explanation?

 

[SaintJude]

I understood that "R1 is longer than R2", was referring to the length of the resistance not the radii. The radii, as they said, are equal.

 

[MedPR]

I understood that "R1 is longer than R2", was referring to the length of the resistance not the radii. The radii, as they said, are equal.

Even so, the equation is P=V^2/R.

Smaller R = bigger Power.

 

[SaintJude]

Touché.

 

[BerkReviewTeach]

This a typical TBR questions.

This is in fact a typical BR question, because it does exactly what the MCAT does by presenting general information in the passage about some topic and then asking you to apply that information to a new and unique setting. The passage may state that (a) with the same current you get the more power drained through a larger resistor (P = I^2R), but that applies to resistors in series. In parallel, you get the same voltage drop (which is why P = V^2R is the better equation). In parallel, current chooses the path of least resistance, which results in greater power drain. It's a deceptively simple concept that we all know, but when applied in a question like this requires a little reasoning to recognize that it's a simple idea.

Touché.

Sometimes questions do that, and in the end you realize how much you can learn from just one little question.