Chapter 27, Problem 047 A copper wire of radius a = 0.307 mm has an aluminum jac

Question

Chapter 27, Problem 047 A copper wire of radius a = 0.307 mm has an aluminum jacket of outer radius b = 0.378 mm. There is a current i = 2.57 A in the composite wire. Take the resistivity for copper and aluminum to be 1.69 x 10 Q-m and 2.75 x 10'Q.m. Calculate the current in (a) the copper and (b) the aluminum. (c) If a potential difference V = 16.2 V between the ends maintains the current, what is the length in meters of the composite wire? (a) Number (b) Number (c) Number 1 Units | 1 Units ]Units

Explanation / Answer

I R = V = same for both cross section

and R = rho L / A

I rho / A = V / L = constant

I1 (1.69 x 10^-8) / (pi (0.307 x 10^-3)^2) = I2 (2.75 x 10^-8) / (pi ((0.378 x 10^-3)^2 - (0.307 x 10^-3)^2))

0.1793 I1 = 0.565 I2

I2 = 0.3171 I1

and I1 + I2 = 2.57 A

I1 + (0.3171 I1) = 2.57

I1 = 1.95 A .....Ans(A)

(B) I2 = 2.57 - I1 = 0.62 A

(C) R1 = V1 / I1 = 16.2 / 1.95 = 8.31 ohm

8.31 = (1.69 x 10^-8) L / (pi (0.307 x 10^-3)^2)

L = 145 m  

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