The resistance of a wire of uniform material and of constant cross sectional are

Question

The resistance of a wire of uniform material and of constant cross sectional area is given by the equation R = rhjo L/A where: rho = resistivity (depends on material and, slightly, on temperature) L = length of the wire A = cross sectional area of the wire. A certain wire of cross sectional area A and length L has a resistance of 250 ohm. For each of the possible changes to it indicated below, determine the new resistance of the wire. Length of wire made 2 L; R =_____ Length of wire made (1/5) L; R =_____ Cross sectional area tripled; R =_____ Cross sectional area made (1/4) its original value; R =_____ Length of wire made 3L and cross section doubled; R=_____ Wire circular in cross section and diameter doubled; R= _____

Explanation / Answer

a)

length is doubled,so resistance also doubles

So, R' = 2*250 = 500 ohm

b)

length is halved

So, R' = 250/2 = 125 ohm

c)

Area is tripled

So, resistance is 1/3 times

So, R' = 250/3 = 83.3 ohm

d)

Area is 1/4 times, So, R' is 4 times

So, R' = 4*250 = 1000 ohm

e)

R' = 3*250/2 = 375 ohm

f)

diameter doubled, so area is 4 times

So, R' = 250/4 = 62.5 ohm

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