Q. 114.0( 5 Votes )

A copper wire of radius 0.1 mm and resistance 1 kΩ is connected across a power supply of 20 V.

(a) How many electrons are transferred per second between the supply and the wire at one end?

(b) Write down the current density in the wire.

Answer :

a) 1.25×1017 b) 6.37×105 A/m2

Given,


Radius of the wire, r= 0.1mm=0.1×10-3m


Resistance of the wire, R= 1000Ω


The voltage across the wire, V= 20V


Formula used,


The wire is having a resistance, R and hence the current, I through it can be found from the equation,



Where V denotes the potential difference across the resistance.


We know that the current, I through a resistor can be calculated from the charge, q flowing through it per seconds, or



Where t is the time in seconds for which the current is flown.


But the charge, q can be written in terms of number of electrons, n flowing by the relation,



Where e is the charge of 1 electron= 1.6×10-19 C


Also, the current density, J through a material with constant area of cross section A, can be represented as



Solution,


a) From the above equations, eqn.1 can be re-written with the help of eqn.2 and eqn.3 as,



Or



For time t= 1s, and by substituting the given values in the above relation, we can calculate the number of electrons passed in 1s through the copper wire with resistance 1000Ω as,




Hence the number of electrons transferred per second between the supply and the wire at one end is 1.25×1017


b)


To find the current density, we have to calculate the area of cross-section, A of the wire with radius r. Hence



By substituting the value for r, we get the area as,



Also, the current through the wire, from eqn.1, is



Now, by substituting the known values in the expression for current density, eqn.4, we get J as



Hence the current density in the wire is around 6.37×105 A/m2


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Electrostatics of ConductorsElectrostatics of ConductorsElectrostatics of Conductors50 mins
Electric DipoleElectric DipoleElectric Dipole46 mins
Test Your Knowledge of Electric Charge & Coulomb's LawTest Your Knowledge of Electric Charge & Coulomb's LawTest Your Knowledge of Electric Charge & Coulomb's Law47 mins
Check your knowledge of Electric Potential | QuizCheck your knowledge of Electric Potential | QuizCheck your knowledge of Electric Potential | Quiz45 mins
Electric field inside cavityElectric field inside cavityElectric field inside cavity37 mins
Electric Flux - TheoryElectric Flux - TheoryElectric Flux - Theory46 mins
Electric Charges and Fields - 05Electric Charges and Fields - 05Electric Charges and Fields - 0556 mins
Relation between electric field and potentialRelation between electric field and potentialRelation between electric field and potential34 mins
Electric Charges and Fields - 08Electric Charges and Fields - 08Electric Charges and Fields - 0854 mins
Electric Charges and Fields - 02Electric Charges and Fields - 02Electric Charges and Fields - 0256 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses