Question

Two cylindrical resistors are made of the same material and have the same resistance. The resistors, R1 and R2, have different radii, r1 and r2, and different lengths, L1 and L2. Which of the following relative values for radii and lengths would result in equal resistances?

a. r1 = r2 and L1 = 2L2
b. 2r1 = r2 and L1 = 2L2
c. r1 = r2 and 4L1 = L2
d. 2r1 = r2 and 4L1 = L2

Answer 1

Answer:

Option d is correct.

Explanation:

We know , resistance of a body is directly proportional to its length and inversely proportional to its area.

$R=\dfrac{\rho\ L}{A}=\dfrac{\rho\ L}{\pi r^2}$      ( Here, $\rho$ is constant dependent on object material )

Writing $R_1 \ and\ R_2$ also :

$R_1=\dfrac{\rho\ L_1}{\pi r_1^2}\ , \ R_2=\dfrac{\rho\ L_2}{\pi r_2^2}$      ( since they are of same material therefore, $\rho$ is same.)

Now , if $r_2=2r_1 \ and \ 4L_1=L_2$.

Then $R_1=R_2$

Therefore, option d. is correct.

Hence, this is the required solution.

Answer 2

The relative values for radii and lengths that result in equal resistances is: (D). 2r1 = r2 and 4L1 = L2

What is resistance ?

Resistance can be defined as the impediment, obstruction, disallowance of current. whatever tends to reduce or stop entirely the free flow of current in a material or body is term resistance.

The resistance of a material is directly proportional to its length and inversely proportional to its area.

In  conclusion,  The relative values for radii and lengths that result in equal resistances is 2r1 = r2 and 4L1 = L2

Learn more about Resistance: https://brainly.com/question/13735984

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