Question

232
Two metallic wires made from
copper have same length but the
radius of wire 1 is half of that of
wire 2. The resistance of wire 1 is R
.If both the wires are joined together
in series, the total resistance
becomes[CDS 2018]

Answer 1

Use the equation R = rho * l / A

Where R = resistance; l = length; A = cross sectional area, rho = resistivity.

Assume the wires are circular cross section.

Wire 1 has resistance R. Wire 2 is the same length, but twice the radius, so 4 times the cross sectional area. So wire 2 has a resistance of R/4.

So total resistance of 2 in series = R + R/4 = 1.25 * R