Question

if the resistance of conducting wire p is four times resiatance of conducting wire Q then the ratio of cross sectional areas of wires are

Answer 1

wireP =4(wireQ) the resistance ATC

r(P)=ρl/a

r(Q)=4(ρL/A)

thus, r(P/Q)=1/4(l/a/L/A)

this is the ratio . i might be wrong.

Answer 2

The relation between resistance and cross-sectional wire is given below:

R= p L/A, where R- Resistance, L= length , A- cross-sectional area of the wire, p- constant

As given: Resistance of P= 4×( Resistance of Q)

For wire P:

R(P) = p L(P)/A(P)---------(1)

For wire Q:

R(Q) = p L(Q)/A(Q)--------(2)

Also given: R(P)= 4R(Q)-----(3)

Dividing (1) by (2), and using the relation(3):

[ L(P) × A(Q) ] / [ A(P) × L(Q) ] = 4

or, A(P) : A(Q) = L(P) : 4 L(Q)--------( Ans )

Therefore we can say that the ratio of cross-sectional areas of the two wires P and Q is equal to the ratio of their lengths in 1:4 ratio.