Question

Out of the two wires P and Q shown below, which one has greater resistance? Justify it.

Answer 1

SoluTion :

✴ Given :-

• Length of wire P = l
• Length of wire Q = l
• Area of cross-section for wire P = A
• Area of cross-section for wire Q = A/2

✴ To Find :-

▪ Which wire has greater resistance...

✴ Concept :-

✈ Resistance of wire is always directly proportional to the length of wire and inversely proportional to the area of cross section of wire.

Mathematically,

$\bigstar\:\boxed{\sf{\pink{\large{R=\rho\times \dfrac{L}{A}}}}}$

• R denotes resistance
• $\rho$ denotes resistivity of wire
• L denotes length of wire
• A denotes area of cross section

✴ Calculation :-

↪ Here, length is same for both wires.

$\sf\:R\propto \dfrac{1}{A}\\ \\ \sf\:\dfrac{R_P}{R_Q}=\dfrac{A_Q}{A_P}\\ \\ \sf\:\dfrac{R_P}{R_Q}=\dfrac{1}{2}\\ \\ \sf\:\red{R_Q=2\times R_P}\\ \\ \boxed{\sf{\purple{\large{R_Q>R_P}}}}$