Question

You want to make a 50Ω resistor from a poorly conducting material that has resistivity 0.020Ωm. The resistor will be a cylinder with a length 5 times its diameter. Current will flow lengthwise through the resistor. Part A What should be its length in cm ?

Answer 1

To make a 50Ω resistor from a poorly conducting material with resistivity 0.020Ωm, you need to calculate the length of the resistor. Use the formula for resistance of a cylinder and substitute the given values to solve for the length.

Step-by-step explanation:

To make a 50Ω resistor from a poorly conducting material with resistivity 0.020Ωm, we can use the formula for resistance of a cylinder:

R = (ρ × L) / A

where R is the resistance, ρ is the resistivity, L is the length of the cylinder, and A is the cross-sectional area.

In this case, we want to find the length of the resistor. Let's assume the diameter of the resistor is x, then the length of the resistor would be 5x.

Since the resistance value is given as 50Ω, the resistivity is given as 0.020Ωm, and we can calculate the cross-sectional area A using the formula:

A = π * (x/2)^2

Now we can substitute the values in the resistance formula and solve for L:

L = (R * A) / ρ

Plugging in the given values, we get:

L = (50 * (π * (x/2)^2)) / 0.020.

Now we just have to solve this equation to find the value of L in cm.