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www.GOALias.blogspot.comCurrentElectricity8. Using E = V/l, I = nev dA, and Ohm’s law, one obtains2eE nevd= ρm mThe proportionality between the force eE on the electrons in a metaldue to the external field E and the drift velocity v d(not acceleration)can be understood, if we assume that the electrons suffer collisionswith ions in the metal, which deflect them randomly. If such collisionsoccur on an average at a time interval τ,v d= aτ = eEτ/mwhere a is the acceleration of the electron. This givesmρ =2ne τ9. In the temperature range in which resistivity increases linearly withtemperature, the temperature coefficient of resistivity α is defined asthe fractional increase in resistivity per unit increase in temperature.10. Ohm’s law is obeyed by many substances, but it is not a fundamentallaw of nature. It fails if(a) V depends on I non-linearly.(b) the relation between V and I depends on the sign of V for the sameabsolute value of V.(c) The relation between V and I is non-unique.An example of (a) is when ρ increases with I (even if temperature iskept fixed). A rectifier combines features (a) and (b). GaAs shows thefeature (c).11. When a source of emf ε is connected to an external resistance R, thevoltage V extacross R is given byεV ext= IR = RR + rwhere r is the internal resistance of the source.12. (a) Total resistance R of n resistors connected in series is given byR = R 1+ R 2+..... + R n(b) Total resistance R of n resistors connected in parallel is given by1 1 1 1R = R + R + ...... +R1 2n13. Kirchhoff’s Rules –(a) Junction Rule: At any junction of circuit elements, the sum ofcurrents entering the junction must equal the sum of currentsleaving it.(b) Loop Rule: The algebraic sum of changes in potential around anyclosed loop must be zero.14. The Wheatstone bridge is an arrangement of four resistances – R 1, R 2,R 3, R 4as shown in the text. The null-point condition is given byR1R3=R2 R4using which the value of one resistance can be determined, knowingthe other three resistances.15. The potentiometer is a device to compare potential differences. Sincethe method involves a condition of no current flow, the device can beused to measure potential difference; internal resistance of a cell andcompare emf’s of two sources.125