Introduction to DC Circuits

This lab is a simple application to Ohm's law, V=IR. We looked at the relationship between voltage, resistance, and current going through a load. Our load has a rating of 0.144 W at 12 V and will function properly as long as we maintain a minimum of 11 V. The battery has a capacity of 0.8 Ahr.

With these assumptions, we need to find the maximum distance the load and battery can be separated using the AWG #30 cable. From this, we need to find the resistance in the cable to ensure we meet the 11 V needed to operate this piece of machinery. In practice, we expect there to be a small drop in voltage and we must account for this, especially with the use of long cables.

The setup consists of a DC power supply measured at 12.10 V to represent the battery, a variable resistor box as the cable resistance, and a 1000 Ω resistor for the load, all hooked up in series. We included an ammeter in series to measure current and a voltmeter parallel to each of these elements to find the voltage.

The setup with the power supply, resistor, and variable resistor box.

The equivalent circuit.

We began by tweaking the variable resistor to get the load as close to 11 V as possible. We found that with the variable resistor at 89 Ω, our load had a potential drop of 11.0 V according to our voltmeter readings.

Our ammeter measured a current of 12.4 mA. With this measurement, and the fact that the battery has a 0.8 Ahr capacity, we calculated that the time it takes to discharge the battery is 64.5 hours.

By using the formula, P = I² R, we calculated the power in the load and the cable. Their values were 0.154 W and 0.0137 W, respectively. The measured power of  0.0137 W therefore does not exceed the power capability of the variable resistor box rated at 1 W (written on the side of the resistor box). With these values, the efficiency of the load comes out to be 91.8 %. This means that the remaining 8.2 % is lost to the cables.

Knowing that the maximum cable resistance can go as high as 89 Ω and assuming we are using AWG #30 wires with a resistance of 0.3451 Ω/m, the maximum distance from the battery to the load is 128.9 m in order to maintain the 11 V needed for the device to remain functional.