Question

if the resistance of conducting wire P is four times resistance of conducting wire Q then the ratio of cross sectional areas of wire is

Answer 1

Resistance is the factor which oppose the conduction of Electricity. Resistance of a wire depends on the cross-sectional area of the wires. As the cross sectional area of a wire increased the electric charge can flow easily therefore the resistance of the wire is decreased. When all other variables (like length of the wire and material of the wire) are the same, resistance of a wire inversely proportional to the cross sectional area of the wire.

Consider the material of two wires are same

The resistance of wire P = $R_{P}$ and the cross sectional area of wire P =$A_{P}$

$R_{P}=\frac{1}{A_{R}}$

The resistance of wire Q = $R_{Q}$ and the cross sectional area of wire P =$A_{Q}$

$R_{Q}=\frac{1}{A_{Q}}$

Given $R_{P}=4\times{R}_{Q}$

The ration of the resistance of two wire

$\frac{R_{P}}{R_{Q}}=\frac{A_{Q}}{A_{R}}\\\\\frac{4\times{R}_{Q}}{R_{Q}}=\frac{A_{Q}}{A_{R}}\\\\\frac{A_{Q}}{A_{R}}=\frac{4}{1}\\\\{A_{Q}}:{A_{R}}=4:1$