Power failure trigger buzzer after some time

Hello there

Im using a phone charger to power up the Arduino and if there is a power failure I want to trigger a buzzer after 1 minute or so..
I kind of managed to do it, but it takes just like 3 seconds to trigger the buzzer, I tried some big capacitors and resistors but had little to no change, 5~8 seconds and the buzzer play too low

Does anyone have any ideia how to make it longer, or if there a better circuit?

(Was thinking about using relay with capacitor in the place where the led is now, it would need to charge the capacitor first in order to trigger the relay, I think, because it wouldn't have enough current/voltage, idk)

(I put an led and resistor in the place of buzzer, I coudnt find it..)

falstad Simulte Circuit

Use a small battery and charge it from the line (phone charger).

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