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I have found a circuit to bass bump headphone amplifier. In the parts list most of the resistors are 1/8 W, but I have only found 1/4W resistors. Will this effect the functioning of the amplifier? Should I increase the battery voltage now?

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The power rating only affects the ability of the resistor to dissipate power as heat. The 1/4W resistors will just be a little larger in physical size (so they can dissipate a higher power), and won't affect the electrical behaviour of this type of circuit.

When you get to very large power ratings then the resistors can change type from carbon/metal film to wirewound and they can have significantly different high frequency behaviour. But you don't have to worry about that in your situation.

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