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
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
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