AC induction controls low power relay?

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I am making a RIAA preamp, opamp based. I'm going to power it from two 9V batteries, but I would like to have the preamp switched on when I power on the record player. The record player uses 120V AC to power the motor.

I'm going to switch the preamp on with a 5V relay that needs 25mA to activate. Because I need so little power for the relay, I would like to not introduce a AC-DC transformer/rectifier into the equation. Is it possible I can 'steal' enough current from the AC power cord by induction, when the unit is powered on?

Or maybe I should just use an AC powered relay?
 
Even if only a little power is needed, better include the transformer for safety reasons: Insulation from the mains circuit.

Induction will not do, unless you decide to wrap the AC line around an iron core with a secondary coil. Guess what you built then... ;)

Rundmaus
 
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