Question

A copper wire of length l and radius r is nickel plated till its radius is 2r. if resistivity is pc and pn, then the equivalent resistence of a wire is

Answer 1

Given:

Length of copper wire = l

Radius of copper wire = r

Radius of nickel wire = 2r

Resistivity = Pc and Pn.

To Find:

Equivalent resistance of the wire

Solution:

Resistivity = Pc and Pn

As R = Pl/A

For Copper = Rc = Pcl/πr ²

For Nickel = Rn = Pnl/ π(4r²-r²)

= Pnl/3πr²

Now, since both are connected in parallel -

RcRn/ Rc + Rn = Pcl/πr ² × Pnl/3πr² / l/πr² ( Pc/1 + Pn/3)

Req = PcPnl²/3 (πr²)² × πr²/l × 3 ( 3Pc + Pn)

Req = PcPnl /  πr² ( 3Pc + Pn)

Answer: The equivalent resistance of wire is  PcPnl /  πr² ( 3Pc + Pn)