Sheet 01 Drift Velocity, Resistance and Conductance, Current Density.
The current I in a circuit varies with time t as per relation given below \(I=5K+3.K^{‘}t\). Find: the constant current which would send the charge equivalent to time interval \(t=0\) to \(t=4s\). Take; constant \(K\) and \(K^{‘}\) as unity.
Ans: \(11A\).
A copper wire has a resistance of \(10\Omega\) and having an area of cross-section \(1 mm^{2}\). A potential difference of \(10V\) exists across the wire. Calculate: the drift velocity of electrons if, the number of electrons per cubic meter in copper is \(8\times10^{28}\) electrons.
Ans: \(0.078m.s^{-1}\).
When a potential difference of \(5V\) is applied across a wire of length \(0.1m\), the dirft velocity of electrons is \(\left(2.5\times10^{-4}\right)ms^{-1}\). If, the number density in the wire is \(\left(8\times10^{28}\right)m^{-3}\). Calculate: the resistivity of material of wire?
Calculate: the electric field in a copper wire having cross-section area \(2.0mm^{2}\) carrying a current of \(1A\). The conductivity of the copper is \(\left(6.25\times10^{7}\right) Sm^{-1}\).
Ans: \(\left(8\times 10^{-3}\right)V.m^{-1}\).
If, free electron density of copper is \(\left(8.6\times10^{28}\right)m^{-3}\) and resistivity of copper at room temperature is \(\left(1.7\times10^{-6}\right)\Omega cm\). Find, the relaxation time for the free electrons of copper. Given: Mass of the one electron = \(\left(9.11\times10^{-31}\right) kg\) and charge on electron = \(\left(1.6\times10^{-19}\right) C\).
A copper wire of length \(2.0 m\), of area of cross section \(2.0 mm^{2}\) carries a current of \(4.0 A\). If, its been assumed that there is one free electron per atom. Atomic mass of copper is \(63g\) and density of copper is \(8.9 g.cm^{3}\). Find: the drift velocity of the electrons in the wire. Also, find: mobility of the electrons if a potential difference of \(100 V\) is applied across the wire.
Ans: \(v_{d}=\left(7.35\times 10^{-5}\right)m.s^{-1}\) and \(\mu=\left(1.47\times 10^{-6}\right) m^{2}.V^{-1}.s^{-1}\).
A potential difference of \(100 V\) is applied to the ends of a copper wire one meter long. Calculate: the average drift velocity of the electrons. Compare it with the thermal velocity at \(27^{o}C\). Given: Conductivity of the copper, \(\sigma_{Cu}=\left(5.81\times10^{7}\right)\Omega m\) and number density of the conduction electrons is, \(n=\left(8.5\times10^{28}\right)m^{-3}\).
(a) Calculate: the average drift velocity of the conduction electrons in a copper wire of cross-section area \(\left(1.0\times10^{-7}\right) m^{2}\), carrying a current of \(1.5A\). Assume that each copper atom roughly contributes one conduction electron. The density of copper is, \(\rho_{Cu}=\left(9.0\times10^{3}\right) kgm^{-3}\), and its atomic mass is \(63.5u\). Take: Avogadro’s Number, \(n=\left(6.023\times10^{27}\right) mol^{-1}\). (b) Compare the drift velocity obtained above with; (i) Thermal speed of copper atoms at ordinary temperature. (ii) Speed of the electrons carrying the current. and
A wire of resistance \(5.0\Omega\) is used to wind a coil of radius \(5 cm\). The wire has a diameter \(2.0 mm\) and the specific resistivity of the wire material is \(\left(2.0\times10^{-7}\right) \Omega m\). Find: Number of turns in coil?
Ans:250.
The external diameter of hollow tube of copper of length \(5m\) is \(10 cm\) and the thickness of the wall of the tube is \(5mm\). If specific resistance of copper is \(\left(1.7\times10^{-8}\right)\Omega m\). Find: the resistance of the tube.
Ans: \(R=\left(5.7\times 10^{-5}\right)\Omega\).
Current flows through a constricted conductor, as shown in figure. The diameter \(D_{1}=2.0mm\) and the current density to the left constriction is \(J=\left(1.27\times10^{6}\right)Am^{-2}\). (I) What current flows into the constriction? (ii) If the current density is doubled as it emerges from the right side of the constriction, what is diameter \(D_{2}\)? Ans:(i) \(I_{1}=3.987A\) and (ii) \(D_{2}=1.414mm\).
