Question

A 3.0 m length of wire is made by welding the end of a 100 cm long silver wire to the end of a 200 cm long copper wire . Each piece of wire is 0.80 mm in diameter. The wire is at room temperature, so the resistivities are as given in the table below. A potential difference of 5.0 V is maintained between the ends of the 3.0 m composite wire.

(a) What is the current in the copper section?. A

(b) What is the current in the silver section? A

(c) What is the magnitude of vector E in the copper? V/m

(d) What is the magnitude of vector E in the silver? V/m

(e) What is the potential difference between the ends of the sliver section of wire? V

Answer 1

Given:

Total length of wire = 3m

Silver length = 1m, Copper length = 2m

diameter = 0.8mm or radius = 0.4 x 10^-3m

Voltage = 5V

Formula to be used:

Solution:

Since the wires are in series, the current through them will be the same. First find the resistances of silver and copper, add them up to find the otal resisitanceo f the circuit. Using the formula V = IR, find the current flowing through it.

a) Resistance of SIlver wire =

Rsilver = 0.029ohm

Resistance of copper =

Rcopper = 0.0685ohm

Total resistance R = 0.0975ohm

V=IR

I = 5/0.0975 = 51.28A

a) current through copper section = 51.28A

b) current through silver section = 51.28A

c) To find the magnitude of of vector E, we use the formula V=EL

since the wires are in series, the voltage across each will be different.

V= IR

V = 51.28 * 0.0685 = 3.513V

To find E,

E = 3.513/2 = 1.76V/m

Ecopper = 1.76V/m

so find the voltage across silver section:

V=IR

V = 51.28A * 0.029 = 1.487V

so, Esilver = 1.487/1 = 1.487 V/m

Esilver = 1.487V/m

e) As calculated earlier , potential difference between ends of silver :

V = 1.487V