Question

The resistance (R) in a wire increases when the length of the wire (L) increases. Write the correct equation for this scenario, and solve for when the length is 1. Length Resistance 10 2 15 3

a. R = 20 over L; R = 20
b. R = .2L; R = 5
c. R = .2L; R = .2
d. R = 20 over L; R = 5

Answer 1

Answer: c. R = 0.2L ; R =0 .2

Explanation:

Given: When length of wire is
`L_1=` 10 units, then resistance of wire
`R_1=`=2 ohm

When length of wire is
`L_2=`15 units, then resistance of wire
`R_2=`=3 ohm

Since, the resistance (R) in a wire increases when the length of the wire (L) increases. Therefore, they are directly proportional.

`(R)/(L)=(R_1)/(L_1)`

`(R)/(L)=(2)/(10)\\\Rightarrow\ R=0.2L`

Now, for Length L=1 unit, we have

`R=0.2(1)=0.2`