Drift Speed of Electrons In a wire

Two wires X and Y have the same resistivity, but their cross sectional areas in the ratio 2:3 and lengths in the ratio 1:2 They are first connected in series and then in parallel to a dc source Find out ratio of drift speeds of electrons in two wires for the two cases.

case i) Series
In series combination current I through each resistor will be the same
Current I= neAVd
n=number of electrons per unit volume
e=Charge of an electron
A=Area of cross section of wire
Vd= Drift speed

Vd= I / (neA)

Vd1= I / (neA1)      --------------(1)
Vd2= I / (neA2)      --------------(2)
Note that 'ne' is same for both the wires since the resistivity same means same material

From 1) and 2) Vd1 / Vd2 = A2 / A1 ie  Ratio of drift speed is 3:2 

 case ii) Parallel
In Parallel combination potential  'v 'through each resistor will be the same
Current I= neAVd
By ohms Law  v=IR
ie v= (neAVd) R
Vd= v / RneA and R=ΡL/A

R1=ΡL1/A1
R2=ΡL2/A2
Ρ=resistivity

Vd1= v / (R1 neA1)---------------(3)
Vd2=  v / (R2 neA1)---------------(4)

From 3) and 4) Vd1 / Vd2 = L2/L1  ie  Ratio of drift speed is 2 : 1


Comments

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