Question
A cylindrical conductor of length L and radius R has its
radius increasing linearly from R at one end to 2R at the other. A constant current I flows through it. If the resistivity of the material is ρ, find the total resistance of the conductor.Solution
To find the total resistance of the conductor, we need to consider a small element of the cylindrical conductor of thickness dx at a distance x from the end with radius R. Let the radius of the conductor at a distance x from the end with radius R be r(x). Since the radius increases linearly from R to 2R over a length L, the rate of increase of the radius with respect to the length is (2R-R)/L = R/L. So, the radius at a distance x is given by: r(x) = R + (R/L)x = R(1+x/L) The cross-sectional area of this small element at distance x is:
What will come in the place of question mark (?) in the given expression?
412 + 25% of 2400 = ? + 1131
What will come in the place of question mark (?) in the given expression?
75% of (√64 × 8 - 16) × ? = 15²
What will come in the place of question mark (?) in the given expression?
(437 + ? - 167) x 2.5 = 875√9604 + ∛205379 + 58% of 1500 = 520 + ?
`(256/6561)(1/4) = ?`
(225 + 125) ÷ 7 + 250 = ? + 20% of 800
9 × 40 × 242 × 182 = ?2
4.7 × 3.5 + 4.2 × 4.5 = 22.5 × 3.5 - ?
31% of 3300 +659 = ?