Battery draining in resistive circuit

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Dark Maggot
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When I was a kid listening to a transistor radio under my pillow late at night I used to wonder whether turning the volume down low would delay the gradual loss of battery voltage. My doubts centered in the fact that the volume control was (at least in those days) a variable resistor. I reasoned that turning down the volume (increasing the resistance) would merely dissipate more EMF in the form of heat, so that the actual work done by the DC cell would be insensitive to changes in the volume setting.

What's the truth of the matter: would listening at low levels prolong useful battery life? If so- where was my childish reasoning faulty?
 
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Welcome to PF! Are you familiar with ohm's law and the definition of power? If you apply them to this situation you may find something counerintuitive about the relationship between resistance and power...
 
Your conclusion was right, but not for the reason you suggest.

The volume control let's you choose how much signal is used to drive the speaker amplifier of the radio. It does this by voltage divider action.

These amplifiers take more power from the battery when they are producing more sound output, so they will use up the battery more quickly if they are delivering more sound.