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what is purpose of using diode across relay coil?

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Take a relay and a battery.
Hold one hand (not two hands) across the relay coil.
Connect the relay coil to the battery then disconnect it.
Your hand will feel the hundreds of volts caused when the current in the inductance of the relay coil suddenly collapses which induces the very high voltage (the flyback voltage).
The hundreds of volts will destroy a transistor that drives the relay coil unless the coil has a reverse-connected diode across it which reduces the voltage spike to 0.7V more than the supply voltage.
 
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