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Question

An aluminum conductor of unknown length with a voltage of 75V is connected in parallel with a copper conductor with same length. When a current of 10A is passed combination, it is found that Determine: 3.1. the length of the copper conductor if the resistively of copper is 0,017 micro-ohm meters and that of aluminum is 2,5mm. micro-ohm meters. 3.2. the current through the copper conductor is 2,5A. the diameter of the aluminum is 2,5mm. the resistance and the diameter of the copper conductor.

Answer 1

(3.1)

Step 1:

The diameter of the aluminum wire is d₁= 2.5 mm.

Let the length of the aluminum wire is l.

Since the length are same, the length of the copper wire is l.

Specific resistivity of the aluminum is .

Specific resistivity of the copper .

Total current in the circuit is i_t = 10 A.

Current through copper wire is i₂ = 2.5 A.

The aluminum wire and copper wire are connected in parallel.

Total Current = i₁ + i₂ .

10 = i₁ + 2.5

i₁  =10 - 2.5

i₁ = 7.5 A.

Current through aluminum wire is i₁ = 7.5 A.

Step 2:

Law of Resistivity:

Resistance offered by a conductor is given by .

Resistance offered by aluminum wire is .

Area of the aluminum wire is .

Resistance offered by aluminum wire is .

Resistance offered by copper wire is .

Area of the copper wire is .

Resistance offered by copper wire is .

Ratio of the resistance is

Answer 2

Contd....(3.1)

Step 3:

In a parallel combination, the voltage across the element are same.

Substitute in equation (1).

Substitute the corresponding values in the above formula.

The diameter of the copper wire is 1.1902 mm.

Step 4:

Find the length of the aluminum conductor .

Resistance of the aluminum conductor .

Voltage drop across the aluminum is .

An aluminum conductor has a voltage of 75V.

Now find the resistance of aluminum conductor.

Substitute resistance of aluminum the .

Length of aluminum conductor is 1.96 km.

So the length of copper conductor is 1.96 km.

Solution :

The length of copper conductor is 1.96 km.

Answer 3

(3.2)

Step 1:

Find the resistance of copper conductor.

Specific resistivity of the copper .

The length of copper conductor l  is 1.96 km.

The diameter of the copper wire is 1.1902 mm.    [From (3.1)]

Resistance offered by copper wire is .

Resistance of the copper conductor is 30 ohms.

Solution :

(a) Resistance of the copper conductor is 30 ohms.

(b) The diameter of the copper wire is 1.1902 mm.