Amplify a signal five times: a schematic puzzle
An op-amp and two resistors set a gain you can read straight off the parts.
An op-amp has one rule: it drives its output to whatever voltage makes its two inputs equal. The signal goes to the + input. The two resistors form a voltage divider that feeds a fraction of the output back to the − input: 10 ÷ (39 + 10), about one fifth. For the − input to match the + input, the output must be five times the input. Gain = 1 + 39 kΩ ÷ 10 kΩ = 4.9. Think of a thermostat set to hold the room at exactly the input temperature; the resistors decide how hard the furnace must run to get there. One limit: on a single 9 V supply the LM358 output can only reach about 7.5 V, so inputs above 1.5 V flatten out.
LM358 op-amp: The thermostat. It has enormous raw gain, around 100 000, but you never use it bare; the feedback resistors tame it to exactly the gain you asked for, and that number stays put with temperature and age.
Feedback resistor, 39 kΩ: The top of the feedback divider. The bigger it is relative to the 10 kΩ, the smaller the fraction fed back and the higher the gain: 1 + 39 ÷ 10 = 4.9.
Gain resistor, 10 kΩ: The bottom of the feedback divider. Shrink it and the gain climbs; leave it out and the gain falls to exactly 1, a voltage follower.