Do you know why the LED glows less brightly when the dimming time is extended? The answer is in the RC time constant.
The RC time constant determines how long it takes the capacitor to discharge, which, in turn, determines how long it takes to dim the LED. To extend the dimming time, you increase either the resistance (the R) or the capacitance (the C), so that the RC time constant is larger. But huge capacitors are hard to find (and very impractical), so increasing the resistance is the better way to greatly extend the dimming time.
Increasing the resistance successfully increases the RC time constant — but it also weakens the current flowing through the LED. (Remember, more resistance means less current.) A very large resistance restricts the current so much that the LED doesn't glow brightly when it's first turned on.What if you wanted to, say, turn on the lights over a stage and then bring down the lights slowly as the curtain opens? Or turn on the dome light in your family's car when you open the car door, and dim the light slowly when you close the car door? The fact that the large resistance produces a weak current can be a problem: The lights won't ever glow brightly — even when they first turn on!
Using a transistor to boost the weak current solves the problem. By placing a transistor between the resistor-capacitor combination and the LED-resistor combination, you essentially jack up the current so that the lights glow brightly when they first turn on!
The way it works is this: You feed the weak current coming from the resistor-capacitor part of the circuit into the base of the transistor. You use that weak base current to control a stronger current flowing from the collector to the emitter, and you use that stronger current to power the LEDs so that they shine brightly (that is, before they dim).This figure lays out your plan of attack for this project. It's useful to visualize what's happening with a block diagram like this because you can easily lose track of the big picture when you start plugging components into the breadboard.