Question

Consider two wires made of the same material:

1)   If both wires have the same radius, but wire 1 is half the length of wire 2, what is the resistance of wire 1 in terms of wire 2?

2) If both wires have the same length, but wire 1 has three times the radius of wire 2, what is the resistance of wire 1 in terms of wire 2?

Answer 1

We know,

R = rho*L/A

R ---> resistance

rho ---> resistivity of materia

L --> length of the wire

A ---> cross sectional area of the wire

1) L1 = L2/2

so, R1 = rho*L1/A

R2 = rho*L2/A

R1/R2 = L1/L2

R1/R2 = (L2/2)/L2

R1 = R2/2 <<<<<<<<----------Answer

2) r1 = 3*r2

r1^2 = (3*r2)^2

r1^2 = 9*r2^2

pi*r1^2 = 9*pi*r2^2

A1 = 9*A2

again take,

R1 = rho*L/A1

R2 = rho*L/A2

R1/R2 = A2/A1

R1/R2 = A2/(9*A1)

R1 = R2/9 <<<<<<<<----------Answer