Introduction To DC Circuits

Motivational Design Problem:

In this exercise we are asked to consider a hypothetical situation where we are to connect a piece of electrical equipment, with specific energy demands, to a battery source that maybe a significant distance away from it. With increasing distance the natural resistance of the connecting wires steadily adds up and this leads to a decrease of the actual power that the electrical equipment will be able to draw. If the total resistance becomes too great then the piece of equipment may no longer function at all.

Design Parameters:

We must determine the maximum distance that the battery and equipment, or load, may be separated from each other if we must connect them by using AWG #30 cable. Also, we are to determine the distribution efficiency and the approximate time before the battery discharges.

We are given that the load is rated to consume 0.144W when supplied with 12V and that it will no longer operate properly when it is supplied with less than 11V. The battery will supply a constant 12V and has a capacity of 0.8Ahr.

System Model:

Above is a photograph of the experimental model which we designed to mimic the demands of the system required by the design problem. It consists of a power supply which is connected in series with a variable resistor box and a mounted resister which simulated our load. We used a multimeter in the circuit to measure the systems amps and another multimeter connected across the load to measure the voltage there.

The variable resistor box allowed us to determine the highest possible resistance which would allow the necessary voltage at the load. By using this highest possible resistance we were able to determine the greatest possible length of cable given the known resistance of AWG #30 cabling.

Results:

We determined that the maximum resistance possible is 142.3 ohms. This allows a maximum cable distance of 412.3 meters connecting the battery source and the load.

It would take the battery about 83.68 hrs to discharge and the system operates at around 92% efficiency.