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 = rho 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; Cross sectional area tripled; Cross sectional area made (1/4) its original value; Length of wire made 3Land cross section doubled; Wire circular in cross section and diameter doubled; R

Explanation / Answer

Here, for R = p * L/A

Now, for the changes

a) as length is doubled , resistance is directly proporational to Length

Rnew = 2 * R = 2 * 250 = 500 Ohm

Rnew = 500 Ohm

b)

length is 1/5 times , resistance is directly proporational to Length

Rnew = 250/5 = 50 Ohm

c)

Area is tripled , as resitance is inversely proporational to area

R = 250/3 = 83.33 Ohm

d)

Area is 1/4 times , as resitance is inversely proporational to area

R = 250 * 4 = 1000 Ohm

e)

NOw, for the new wire

Rnew = 3 * R/2 = 1.5 * 250

Rnew = 375 Ohm

f) as diameter is doubled , A = pi * d^2/4

area will be 4 times

Rnew = 250/4 = 62.5 Ohm

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