Ohm's law specifies the relationship between voltage (V), current (I), and resistance (R) in an electrical circuit: V = IR.

Solved for resistance, R = \( \frac{V}{I} \) = \( \frac{45}{0.5} \) = 90 Ω

Connecting the 4 batteries in series multiplies their voltage while keeping their current the same yielding a 48V 15A configuration. Connecting the 4 batteries in parallel multiplies their current while keeping their voltage the same yieleding a 12V 60A configuration. Using a series-parallel connection, 2 batteries can be connected in series and 2 can be connected in parallel resulting in a 24V 30A configuration.

All conductors have resistance and the amount of resistance varies with the element.  But, resistance isn't the only consideration when choosing a conductor as the most highly conductive elements like silver and gold are also more expensive and more brittle than slightly less conductive elements like copper. A balance needs to be struck between the electrical qualities of a material and its cost and durability.

An amplifier is a device that takes a small input signal and creates a larger output signal. This makes it most similar to a step-up transformer which takes a smaller input voltage and creates a larger output voltage.

Current flow through a wire increases the temperature of the wire. If too small a wire is used, the wire will heat up causing a loss in conductivity and possibly a fire. The thicker in diameter a wire is, the more current it can carry without overheating.