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Explain electromagnetic induction and calculate the number of turns on the secondary coil of a transformer given primary voltage, secondary voltage, and primary turns.

Physics

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Answer

b

273\text{273}

Step-by-step solution

3 steps

Here's the solution:

Part a

When the magnet spins, the magnetic field lines passing through the coil change continuously. This change in magnetic flux linkage through the coil induces an electromotive force (e.m.f.) across the coil, according to Faraday's Law of Electromagnetic Induction. The voltmeter measures this induced e.m.f., resulting in a reading.

Part b

273\text{273}

  1. Identify the given values.

    Primary voltage, Vp=220 VV_p = 220 \, \text{V}
    Secondary voltage, Vs=12 VV_s = 12 \, \text{V}
    Number of turns on the primary coil, Np=5000N_p = 5000 turns
    Number of turns on the secondary coil, Ns=?N_s = ?

  2. Use the transformer equation.

    The relationship between voltage and the number of turns in a transformer is given by:

    VpVs=NpNs\frac{V_p}{V_s} = \frac{N_p}{N_s}

  3. Substitute the values and solve for NsN_s.

    220 V12 V=5000Ns\frac{220 \, \text{V}}{12 \, \text{V}} = \frac{5000}{N_s}

    Rearrange the equation to solve for NsN_s:

    Ns=12 V220 V×5000N_s = \frac{12 \, \text{V}}{220 \, \text{V}} \times 5000 Ns=12220×5000N_s = \frac{12}{220} \times 5000 Ns=60000220N_s = \frac{60000}{220} Ns=600022N_s = \frac{6000}{22} Ns=300011N_s = \frac{3000}{11} Ns≈272.727N_s \approx 272.727

    Rounding to a whole number of turns:

    Ns=273N_s = 273

    The number of turns on the secondary coil is 273\boxed{\text{273}}.

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