Resistivity example in BR Physics

[MedalHead15]

In Example 9.2b, the question states:

For the following data, what is the ratio of the resistivities of resistor A to resistor B?

Resistor A:
R (k-Ohms) = 2, radius (mm) = 1, L (cm) = 3

Resistor B:
R (k-Ohms) = 4, radius (mm) = 2, L (cm) = 6

A. 4:1
B. 2:1
C. 1:2
D. 1:4

The answer is D, but using the equation for resistance, R=(rho*L)/A, I keep getting a 2:1 ratio, or answer choice B. Any idea what I'm doing wrong?

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[PhilIvey]

In Example 9.2b, the question states:

For the following data, what is the ratio of the resistivities of resistor A to resistor B?

Resistor A:
R (k-Ohms) = 2, radius (mm) = 1, L (cm) = 3

Resistor B:
R (k-Ohms) = 4, radius (mm) = 2, L (cm) = 6

A. 4:1
B. 2:1
C. 1:2
D. 1:4

The answer is D, but using the equation for resistance, R=(rho*L)/A, I keep getting a 2:1 ratio, or answer choice B. Any idea what I'm doing wrong?

R=p(L/A) (A/L)R=p
2/3=p for the 2 ohm
8/3=p for the 4 ohm You don't need to convert units. However, you can't forget to square the radius since it's Area and they gave you radius.
2/3: 8/3= 1:4

 

[Vanguard23]

Square the radius. And, I'm not sure about current, but flow rate(in a pipe) is radius to the fourth power and not second power; meaning doubling a radius will increase the flow rate 16 times instead of 2 times or 4 times. Keep that in mind.

 

[BerkReviewTeach]

In Example 9.2b, the question states:

For the following data, what is the ratio of the resistivities of resistor A to resistor B?

Resistor A:
R (k-Ohms) = 2, radius (mm) = 1, L (cm) = 3

Resistor B:
R (k-Ohms) = 4, radius (mm) = 2, L (cm) = 6

A. 4:1
B. 2:1
C. 1:2
D. 1:4

The answer is D, but using the equation for resistance, R=(rho*L)/A, I keep getting a 2:1 ratio, or answer choice B. Any idea what I'm doing wrong?

The problem might be that if you look at the table a second time, you'll see that A has a resistance of 2 ohms and B has a resistance of 4 ohms, so you need to account for that ratio.

Resistor A:
2 (k-Ohms) = 2, radius (mm) = 1, L (cm) = 3

Resistor B:
4 (k-Ohms) = 4, radius (mm) = 2, L (cm) = 6

RB/RA = 4/2 = (rhoB X LB)/AB / (rhoA X LA)/AA

Substituting 4AA = AB and 2LA = LB gives:

2 = (rhoB X 2LA)/4AA / (rhoA X LA)/AA = rhoB/rhoA x 2/4

rhoB/rhoA = 2 x 2 = 4 : 1

The question asks for A : B, so the ratio is 1 : 4.