State Faraday's law of electromagnetic induction. Describe an experiment to demonstrate this law. Derive an expression for the effective resistance of two resistors in parallel. A coil consists of 150 turns of wire and has a total resistance of 200 Ω. It is connected in series with a 120 V d.c. power supply and a parallel combination of a 200 Ω and a 50 Ω resistor, as shown. Calculate the current in (i) the coil (ii) the 50 Ω resistor. The d.c. supply is then replaced with an a.c. supply. It takes 3 ms for the magnetic flux cutting the coil to increase by 4.5 × 10⁴ Wb. The average voltage of the a.c. supply during this time period is 120 V. Calculate (i) the average emf induced in the coil during the 3 ms time period (ii) the average current in the coil during this period.

Leaving Cert Physics Electromagnetic Induction: State Faraday's law of electroma

State Faraday's law of electromagnetic induction - Leaving Cert Physics - Question 10 - 2016

Question 10

State Faraday's law of electromagnetic induction. Describe an experiment to demonstrate this law. Derive an expression for the effective resistance of two resistors... show full transcript

Worked Solution & Example Answer:State Faraday's law of electromagnetic induction - Leaving Cert Physics - Question 10 - 2016

Step 1

State Faraday's law of electromagnetic induction.

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Answer

Faraday's law of electromagnetic induction states that the electromotive force (emf) induced in a coil is proportional to the rate of change of magnetic flux through the coil. The equation can be expressed as:

ext{emf} = - rac{d heta}{dt}

where ( heta ) is the magnetic flux.

Step 2

Describe an experiment to demonstrate this law.

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Answer

To demonstrate Faraday's law, one can set up an experiment with a coil wrapped around a magnet. By moving the magnet quickly in and out of the coil, an emf is induced, which can be measured with a galvanometer. The faster the magnet moves, the greater the reading on the galvanometer, demonstrating that a change in magnetic flux induces current.

Step 3

Derive an expression for the effective resistance of two resistors in parallel.

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Answer

The effective resistance ( R_{eq} ) of two resistors in parallel, ( R_1 ) and ( R_2 ), can be derived using the formula:

\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}

By rearranging, we obtain:

R_{eq} = \frac{R_1 \cdot R_2}{R_1 + R_2}

Step 4

Calculate the current in (i) the coil.

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Answer

For the coil, using Ohm's law, we can find the current ( I_c ):

R_{total} = 200 \Omega \ V = 120 V \ I_c = \frac{V}{R_{total}} = \frac{120}{200} = 0.6 A

Step 5

Calculate the current in (ii) the 50 Ω resistor.

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Answer

The effective resistance of the parallel combination is given by:

R_{parallel} = 40 \Omega \ R_{total} = R_{coil} + R_{parallel} = 200 + 40 = 240 \Omega

Using Ohm's law, the current through the 50 Ω resistor can be calculated as:

I_{50} = \frac{120}{R_{parallel}} = \frac{120}{40} = 3 A

Step 6

Calculate (i) the average emf induced in the coil during the 3 ms time period.

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Answer

The average emf ( \mathcal{E} ) induced can be calculated using the formula:

\mathcal{E} = \frac{\Delta \theta}{\Delta t} = \frac{4.5 \times 10^{4}}{3 \times 10^{-3}} = 15000 V

Step 7

Calculate (ii) the average current in the coil during this period.

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Answer

The average current in the coil can be found using Ohm's Law:

I_{coil} = \frac{\mathcal{E}}{R_{coil}} = \frac{15000}{200} = 75 A

State Faraday's law of electromagnetic induction - Leaving Cert Physics - Question 10 - 2016

Worked Solution & Example Answer:State Faraday's law of electromagnetic induction - Leaving Cert Physics - Question 10 - 2016

State Faraday's law of electromagnetic induction.

Describe an experiment to demonstrate this law.

Derive an expression for the effective resistance of two resistors in parallel.

Calculate the current in (i) the coil.

Calculate the current in (ii) the 50 Ω resistor.

Calculate (i) the average emf induced in the coil during the 3 ms time period.

Calculate (ii) the average current in the coil during this period.

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