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Two cylindrical rods, one copper and the other iron, are identical in lengths and cross-sectional areas. They are joined, end to end, to form one long rod. A 12-V battery is connected across the free ends of the copper-iron rod. What is the voltage between the ends of the copper rod?

Respuesta :

usmanbiu

Answer:

Vc = 2.41 v

Explanation:

voltage (v) = 16 v

find the voltage between the ends of the copper rods .

applying the voltage divider theorem

Vc = V x ([tex]\frac{Rc}{Rc + Ri}[/tex])

where

  • Rc = resistance of copper = [tex]\frac{ρl}{a}[/tex]  (l = length , a = area, ρ = resistivity of copper)
  • Ri = resistance of iron = [tex]\frac{ρ₀l}{a}[/tex]  (l = length , a = area, ρ₀ = resistivity of copper)

Vc =  V x ([tex]\frac{\frac{ρl}{a}}{\frac{ρl}{a} + \frac{ρ₀l}{a}}[/tex])

Vc = V x ([tex]\frac{ρ x (\frac{l}{a})}{(ρ + ρ₀) x (\frac{l}{a})}[/tex])

Vc = V x ([tex]\frac{ρ}{ρ + ρ₀}[/tex])

where

  • ρ = resistivity of copper = 1.72 x 10^{-8} ohm.meter
  • ρ₀ = resistivity of iron = 9.71 x 10^{-8} ohm.meter

Vc = 16 x ([tex]\frac{1.72 x 10^{-8}}{1.72 x 10^{-8} + 9.71 x 10^{-8}}[/tex])

Vc = 2.41 v

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