Introduction to DC Circuit

Purpose


The purpose of this lab is to determine the maximum permissible cable resistance required for the load to still function normally, and the maximum distance the battery and load can be separated if use AWG # 30 cable, the distribution efficiency, and the approximate time before the battery discharge. The simple system can be illustrated as following

Figure 1. A Simple Cabling System

1. The theoretical value for R(load) can be determined by using R=V^2/(P)= 12^2/0.144=1 Kohm.
2. Since we need to measure the current through the circuit and the voltage across R(load), ammeter and voltmeter need to be inserted into circuit in series and parallel respectively.
3. The resistor box power rating is 0.3 W and the max supply voltage and current are 12 V and 2 A.
4. Based on the value of the resistor, we choose "Brown black red gold" resistor to act as R(load) which provides us 1000 ohm within 5 % error, and its real measured value is 980 ohm. Also, its wattage is 0.25 W. For R(cable), the measured value is 87.3 ohm and its theoretical value is 88 ohm. Its wattage is 0.3 W from the label.
5. We measure the actual voltage which is 12.09 V that a 12 V power supply can really provide.
6. Next, we build the circuit as following
7. Then we measured V(load)=11.1 V, I(Bat)=11.3 mA, and R(cable total)= 87.3 ohm.
8. We use the Ahr capacity of the battery  to estimate the amount of time the battery can supply this load before being discharged. The capacity of the battery is 8 Ahr. By calculation, 8 Ahr= 11.3mA*t therefore, t = 708 hr.
9.  Moreover, we want to know distribution efficiency of this circuit, so we have to calculate power to   the load and to the cable. P(load)=11.1^2/980=0.126 W, and P(cable) =(12.0911.1)^2/87.3=0.0112 W. The efficiency is p(out)/(P(out)+P(lost))=0.126/(0.126+0.0112)*100 = 91.8 %
10.  If we have a AWG #30 wire which the resistance is 0.3451 ohm/m. we can determine the maximin  distance between the battery and the load. That is 1/2 * 87.3 ohm/0.3451 ohm/m = 126.5 m

Figure 2. Actual simple circuit