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What would happen if we use DC source instead of AC source in mutual induction?

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Using a DC source in mutual induction would result in no induced voltage in the secondary coil after the initial moment of connection. Mutual induction relies on changing magnetic fields to induce voltage. With DC, the magnetic field stabilizes once the current reaches a constant level, so the secondary coil would only experience a brief induction when the DC is first applied or removed.
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In mutual induction, the changing magnetic field created by an alternating current (AC) in one coil induces a voltage in a nearby coil. This phenomenon relies on the fact that the magnetic field produced by the AC source is continuously changing, which induces an electromotive force (EMF) in the secondary coil.

If you use a direct current (DC) source instead of an AC source:

1. **Constant Magnetic Field**: A DC source produces a constant current, which generates a constant magnetic field. This means there is no change in the magnetic flux over time.

2. **No Induced EMF**: According to Faraday's Law of Induction, an EMF is induced in the secondary coil only when there is a change in the magnetic flux through it. Since a DC current creates a steady magnetic field (with no change), no changing flux occurs, and thus no EMF is induced in the secondary coil.

3. **Initial Surge**: If you suddenly switch on or off a DC source, there will be a brief moment where the magnetic field changes, and a small EMF might be induced during this transition period. However, once the DC current is stable, the induced EMF will drop to zero.

In summary, a DC source does not continuously induce voltage in the secondary coil due to the lack of a changing magnetic field. AC is essential in mutual induction to maintain a fluctuating magnetic field that induces a steady voltage in the secondary coil.
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