Question

two wires A and B are equal lengths different cross sectional areas and made of the same metal first name the property which is same for both the wire second name the property which is different for both the wires third if the resistance of wire is 4 times the resistance of wire B calculate a the ratio of the across sectional areas of the wires be the ratio of the red eye of the wires​

Answer 1

Heya!!

1) Resistivity is same for both the wires as the material used in both the wires is same.

2) Resistance is Different for both the wires,as resistance depends on Area of cross section.

3) let the length of wire A be = xm

And

let the length of wire B be = ym

According to the given Question

x = y

let x = y = L

R = q L/A

Where R is resistance, q is resistivity,L is length And A is Area of cross Section.

For Wire A let it's Cross sectional area be A1 And let it's Resistance be R1

And

For Wire B let it's Cross sectional area be A2. And let it's resistance be R2

According to the given Question

R1 = 4 R2 ( Given )

Now, use the relation R = q L/A

For Wire A

R1 = q L/A1

4 R2 = q L/A1 ... Equation i

For wire B

R2 = q L/A2 ... Equation ii

Now, Divide both the Equations we have.

4R2/R2 = A2/A1

4 = A2/A1

A2 : A1 = 4 : 1

So, The ratio of their cross sectional area is 4 : 1 Respectively.