Question

Two wires having the same resistivity have their lengths in the ratio 2: 1. Find the ratio of their areas of cross-section

Answer 1

Answer:

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