this Gain formula is associated with amplifier circuits and I think you have a slightly different formula than what is normally used...
by Vs you mean supply voltage, this can cause confusion since the supply voltage of an amplifier circuit doesn't actually have a direct relation with the gain
the proper solution would be gain = Vout/Vin
the Vs is the voltage you apply to the amplifier to make it work, the Vin is the input voltage you apply to the working amplifier and the Vout is the amplified voltage
Vs is not always the Vin of your circuit
for example, a usb-speaker, your Vs in this case is the voltage provided by the usb port w/c is 5V, the Vin is the voltage coming from your audio jack, and the Vout would be the voltage across the speaker
by Vs you mean supply voltage, this can cause confusion since the supply voltage of an amplifier circuit doesn't actually have a direct relation with the gain
the proper solution would be gain = Vout/Vin
the Vs is the voltage you apply to the amplifier to make it work, the Vin is the input voltage you apply to the working amplifier and the Vout is the amplified voltage
Vs is not always the Vin of your circuit
for example, a usb-speaker, your Vs in this case is the voltage provided by the usb port w/c is 5V, the Vin is the voltage coming from your audio jack, and the Vout would be the voltage across the speaker
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IT would represent the voltage across the load, like a speaker.