Question

Question:

The electrical resistance (R) of a
wire varies directly as its length (I)
and inversely as the square of its
diameter (d). A wire with a length
of 5.0 m and a diameter of 0.25
cm has a resistance of 20 Q
(ohms). Find the electrical
resistance in a 10 m long wire that
has twice the diameter.

Answer 1

Explanation:

R =
`(KL)/(d^(2) )` ------ equ.1

given R= 2O, L = 5.Om = 500cm, d = 0.25cm. substituting the given data into the above equation,

20 =
`(500k)/((0.25)^(2) )`

20 =
`(5.0K)/(0.0625)`

50OK = 20 x 0.0625

K =
`(20*0.0625)/(500)`

K = 0.0025

substituting value of K into equ. 1

R =
`(0.0025L)/(d^(2) )`

(from the second part of question, R = 10m = 1000cm, d = 2 x 0.25 = 0.5cm)

R =
`(0.0025*1000)/((0.5)^(2) )`

R = 10