Lab 1: Introduction to DC Circuits

Objective:

The purpose of this lab is to determine the maximum permissible cable resistance required to allow the load to function normally, the maximum distance the battery and load can be separated if an AWG #30 cable is used, the distribution efficiency of the circuit, and the approximate time for the battery to discharge.

The figure above is the original schematic of the experiment.  The figure below is the schematic set-up used to model the original schematic, with RcableTot representing the cables.  

Model:

To model the second schematic in the objective section, a power supply is used to represent the battery, a resistor of known resistance, 1000 Ω, represents the "Load", and a resistor box to represent the unknown resistance of the cables.  An ammeter is set in series with the circuit to measure the total current circulating within the circuit.  The voltmeter is placed in parallel with the "Load", the 1000 Ω resistor, to measure the voltage across it.  

Data:

Known Values:

PLoad = 0.144W when supplied 12V

Capacity rating of battery = 0.8 Ahr

Resistor Box Power Rating = 1 W

Theoretical Value :

RLoad = V^2/P = (12 )^2/ 0.144 = 1000 Ω

Measured Values:

VBattery = 12.28V

IBattery = 11.19 mA = 11.19*10^-3 A
RLoad = 990 Ω
VLoad = 11.01 V

RCableTot = 100.9 Ω

Analysis/Calculations:

Time to Discharge a 0.8Ahr battery capacity circuit:

Amp-Hr = Amps * Time

Time = (0.8 Ahr)/ 11.19*10^-3 A = 71.49.24 hr ≈ 71.49 hr

Distribution Efficiency of Circuit:

Power = V^2/R = I^2*R

PLoad = Pout = I^2*R =  (11.19*10^-3 A)^2 * (990 Ω) = 0.123964 W

PCableTot = PLost =  I^2*R =  (11.19*10^-3 A)^2 * (100.9 Ω) = 0.012634 W

Efficiency = POut/(POut+PLost) * 100 = (0.123964 W)/( 0.123964 W + 0.012634 W) * 100 ≈90.75%

For the resistor box used in this experiment, the power rating of the box is 1 W and the power calculated for PCableTot (the resistor box) is 0.012634 W.  It can be concluded that the experiment did not exceed the power capability of the resistor box since PCableTot is less than the power rating on the resistor box.

The total maximum distance between the battery and the load with a AWG #30 wire:

Maximum Distance  = RCableTot/(2*RAWG#30) = 100.9 Ω/ (2*0.3451 Ω/m) = 146.19 m