Resistance of a wire is directly proportional to its

Asked by admin @ 13/08/2021 in Math viewed by 316 People

The resistance of a wire, R ohms (Ω), is directly proportional to its length, l

m, and inversely proportional to the square of its radius, r m.
(a) Make r the subject of the formula.
(b)Given that a wire with a length of 8 m and a radius of 1 cm has a
resistance of 40 Ω, find the value of k.

Answered by admin @ 13/08/2021

Step-by-step explanation:

R ∝ l

R ∝ 1/r²

combining

so, R ∝ l/r²

R = kl/r² (where k is constant which

is known as Resistivity)

(a) r = ✓(kl/R)

(b) through the given imformation

l = 8m, r = 1cm and R = 40Ω

So, using the formula, R = kl/r²

40 = k×8/1²

k = 5Ω-m

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