The transistor is the foundation of modern electronic devices. It is made entirely from semiconductor material (making it a solid state device) and can serve many different functions in a circuit including acting as a switch, amplifier, or current regulator. A transistor works by allowing a small amount of current applied at the base to control general current flow from collector to emitter through the transistor.

You can multiply the voltage or the current supplied by individual batteries by connecting them together either in series or in parallel. The characteristics of batteries connected in series are that total voltage equals the sum of the individual battery voltages, total current equals the average of the individual battery currents, the positive terminal of one battery is connected to the negative terminal of the next, and one connection is made between each adjacent battery.

Resistors are used to limit voltage and/or current in a circuit and can have a fixed or variable resistance.  Variable resistors (often called potentiometers or rheostats) are used when dynamic control over the voltage/current in a circuit is needed, for example, in a light dimmer or volume control.

Connecting the 10 batteries in series multiplies their voltage while keeping their current the same yielding a 60V 20A configuration. Connecting the 10 batteries in parallel multiplies their current while keeping their voltage the same yieleding a 6V 200A configuration. Using a series-parallel connection, 5 batteries can be connected in series and 5 can be connected in parallel resulting in a 30V 100A configuration.

Semiconductors have valence shells that are exacly half full and can conduct electricity under some conditions but not others. This property makes them useful for the control of electrical current.