Two conductors are made of the same material and have the same length. Conductor A is a solid wire of diameter 1mm. Conductor B is a hollow tube of outer diameter 2mm and inner diameter 1mm. Find the ratio of resistance RA to RB.
NCERT Class XII
Physics - Exemplar Problems
Chapter 3. Current Electricity
Answers
length of two conducting wires are same and both are made of same material
means, resistivity of wires are same.
we know the formula of resistance ,
R = pl/A
where p is resistivity, l is length and A is cross sectional area of wire.
here l and p are constant
so, R is inversely proportional to A.
cross sectional area of conductor A = πr² = π(1mm)² = π mm²
cross sectional area of conductor B = π(R² - r²) = π[(2mm)² - (1mm)² ] = 3π mm²
so now ratio of resistance of wires = π/3π= 1/3
hence, answer is 1:3
Answer:
3:1
Explanation:
radius of wire A = 1/2mm = 0.5 mm
radii of wire B = 2/2 and 1/2 = 1mm and 0.5 mm
resistance is inversely proportional to area.
Area of wire A = π[radius of A]² = 0.25π
area of wire B = π[1² - 0.5²] = 0.75π
RATIO OF AREA = 0.25π/0.75π = 1/3
RATIO OF RESISTANCE = 1/ratio of area = 3:1