This circuit is supplied as a hobby project.
This project circuit is designed to give an automobile's interior lights a fading delay before turning off. When the car door is open, the normally open car door contact switch is open and on. By design, that charges the 22uF capacitor fully. (That capacitor can be varied slightly for various reason.) The 741 opamp IC behaves as a voltage follower and the output from it is the same as the voltage across the capacitor, which is about 12 to 13.8 volts when the capacitor is fully charged, depending on the alternator's output. Due to a high voltage at the output of the IC, the transistor saturates, turning the bulb on to full brightness by supplying full voltage. In the opposite state, the door switch is pushed in, closed, turning the power off. When the switch is in the off position, the capacitor starts discharging slowly through VR1 and the 10K resistor. The residual voltage across it decreases slowly. The output of IC 741 also the voltage decreases gradually, decreasing the base current to the transistor. This yields a slowly decreasing current through the bulb and the bulb fades in brightness until it is no longer visible. When the capacitor is fully discharged, the bulb turns off. Subsequent to the circuit construction, with the switch on, adjust the preset VR2 to the desired initial brightness of the bulb. Then engage the door switch to the off position and adjust VR1 for the time to bring the bulb from full brightness to off. At full values on VR1 and VR2, this gives an adequate time to leave the car at night but still have some light to see as you exit the vehicle. The 2N3055 power transistor is taking a heavy load and generating heat. It needs a large and adequate heat sink.