Consider two cylindrical conductors made ofthe same ohmic material. Conductor 1

Question

Consider two cylindrical conductors made ofthe same ohmic material. Conductor 1 has a
radius r1 and length l1 while conductor 2 has
a radius r2 and length l2.
Denote: The currents of the two conductors
as I1 and I2, the potential differences between
the two ends of the conductors as V1 and V2,
and the electric fields within the conductors
as E1 and E2.

If ?2 = ?1 , r2 = 2 r1 , l2 = 3 l1 and V2 =
V1 , find the ratio
R2
R1
of the resistances.
1.R2/R1= 4
2.R2/R1= 2
3.R2/R1=3/4
4.R2/R1=1/4
5.R2/R1=4/3
6.R2/R1=2/3
7.R2/R1=1/2
8.R2/R1=1/3
9.R2/R1=3/2
10.R2/R1=3

Explanation / Answer

The relation between resistance and resistivity is given by
R = /A = / r^2
Then since r2 = 2 r1 and 2 = 3 1, the ratio
of the resistances is
R2/R1 = ( 2 / r2^2) / ( r1^2 / 1)
R2/R1 = 2 r1^2 / 1 r2^2

R2/R1 = (3 1) r1^2 / 1 (2 r1)^2

R2/R1 = 3/4

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---