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Question

Answer 1

Step 1 :

2.1.1)

Two capacitors are in series.

Substitute  microfarads,  microfarads.

Total capacitance is 6 microfarads.

Solution :

Total capacitance is 6 microfarads.

Answer 2

Step 1:

2.1.2)

From (2.1.1), total capacitance is 6 microfarads.

Find the potential difference across each capacitance.

Now find the total charge .

.

Substitute and in the total charge.

The total charge is

Find the voltage across the capacitance .

Find the voltage across the capacitance .

The voltage across the capacitors  are and .

Solution :

The voltage across the capacitor is .

The voltage across the capacitor is .

Answer 3

2.2)

Lenz's law :

Lenz's law states that when an emf is generated by a change in magnetic flux according to Faradays's Law , the polarity of the induced emf is such, that it produces an current whose magnetic field opposes the change which produces it.

The negative sign used in Faraday's law of electromagnetic induction, indicates that the induced emf  and the change in magnetic flux have opposite signs.

Where is Induced emf,

         is change in magnetic flux,

           is no of turns in coil.

Answer 4

Step 1:

Length of the aluminium is 22 m.

The diameter of the aluminum wire is d₁= 4 mm.

Since the length are same, the length of the copper wire is 22 m.

Specific resistivity of the aluminum is .

Specific resistivity of the copper .

Total current in the circuit is i_t = 25 A.

Current through copper wire is i₂ = 15 A.

The aluminum wire and copper wire are connected in parallel.

Total Current = i₁ + i₂ .

25 = i₁ + 15

i₁  =25 - 15

i₁ = 10 A.

Current through aluminum wire is  i₁ = 10 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

Comments

Contd...

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 3.817 mm.

Solution :

(2.3.1) The diameter of the copper wire is 3.817 mm.

Answer 5

(2.3.2)

Step 1:

(b)

Specific resistivity of the aluminum .

Specific resistivity of the copper .

Voltage drop across the aluminum is .

Current through copper wire is i₂ = 15 A.

Current through aluminum wire is  i₁ = 10 A.

The diameter of the aluminum wire is d₁ = 4 mm.

The diameter of the copper wire is d₂ = 3.817 mm.

Resistance offered by aluminum wire is .

Resistance offered by aluminum is .

Voltage drop across the aluminum:

Voltage drop across the aluminum is 0.2229 v.

In a parallel combination, the voltage across both the elements are same.

Voltage drop across the copper is 0.2229 v.

Solution:

Voltage drop across the conductors is  0.2229 v.

Answer 6

Step 1:

(2.4)

A coil has a resistance 125 ohms at 50 °C.

Resistance of the coil increases 250 ohms at 300 °C.

Find the temperature coefficient of the conductor.

Therefore the temperature coefficient is 0.004 per °C.

Solution :

The temperature coefficient is 0.004 per °C.