There are 4 answers since there is a part A, B, C, and D A cylindrical conductor

Question

There are 4 answers since there is a part A, B, C, and D

A cylindrical conductor has resistance of R_0 = 570 ohm. It has length l, radius of the cross section r, and resistivity g. Express the resistance in terms of l, r, g If the resistivity increases by a factor of 5, what would the value of the new resistance be, in ohms? If the length of the conductor decreased by a factor of 5, what would the value of the new resistance be, in ohms? If the radius of the conductors increased by a factor of 7, what would be the value of the new resistance, in ohms?

Explanation / Answer

a) For a cylindrical shaped conductor of the resistance(R),resistivity(p),length(l),area of cross section (A) are related as

R=pl/A   

that shows R0=570ohm=pl/A

b) If resistivity is increased by a factor of 5 then new value of resistivity(p1) will be 5p

that shows new resistance(Rb=5pl/A) i.e; Rb=5R0=5*570=2850ohm

Here ,the assumption is length,area of cross section remains constant {only resistivity of material changes}

c)Similar to above question if length decreses by a factor 5 new value of length(l1) will be l/5

that shows new resistance [Rc=(p/A)*(l/5)] i.e; Rc= R0/5 =570/5 =114ohm.

Here the assumption is p and A doesn't change

d) As the conductor is cylindrical the area of cross section is circular in shape and its magnitude is = r2

that shows R0=pl/(r2 ) ; now the radius is increased by factor 7 then the new area of cross section(A1) =*(7r)2 = 49r2 ; that implies the new resistance Rd = pl/49A=R0/49 = 570/49 = 11.6326 ohm

Here the assumption i onlt the area changes.

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