Introduction to DC Circuits

Introduction
     In this experiment, we assume some value for resistance, power and permissible voltage drop for a load. We want to determine the permissible cable resistance so that the load can function normally. We would like to be able to determine the maximum distance the battery and the load can be separated if we use different types of cable. We will also determine the battery life and the efficiency.



Experiment
We first creates assumptions:

• Load is rated to consume 0.144W when 12V is supplied
• The voltage drop across load has to be more than 11V
• Battery voltage remain constant at 12V and has capacity of 0.8Ahr

Once the assumptions were made, the theoretical value for R can be calculated as follow:

R = V² / P

R = 12² / 0.144W

R = 1000Ω

After the theoretical resistor was calculated, a resistance box with power rating of 0.3W is used to become the representation of resistance of cable. The power supply rating have a maximum supply voltage of 12V and max current of 2A. The resistance box was also adjusted so that the voltage drop across the load is 11V.

The resistor used for the experiment are listed below:

Element	Nominal Value (Ω)	Measured Value (Ω)	Tolerance?	Wattage
Load	1000	980	Yes	0.25
Cable	88	87.3	Yes	0.3

The voltage of the power source was measured and comes out to be 12.09 ± 0.005 V

Once every element have been measured and calculated, the circuit was set up as follow:

Setup of the lab and the measurement of voltage drop across load

As seen in the picture and also several measurement,some data are achieved:

     V_load = 11.1 V

      I_battery = 11.3 mA

     R_cable = 87.3 Ω

After the data is taken, battery life can be determined by using:

     Battery capacity = current*time

     Time = Battery Capacity / Current

              = 0.8 A-hr / 0.0113 A

              = 70.80 hr

Power was also calculated in this lab and turns out as follow:

    P = V²/R = I²R

    Power to the load = 0.126 W

    Power to the cable = 0.0111 W

Once the power is calculated, the efficiency is also calculated using the following formula:

      η = [ P_out / (P_out + P_lost) ] * 100

      η = 91.9%

Questions

1. In one of the question, the total power is not exceeding the power capability of resistor box since the total power used is around 0.1W but never exceed the 0.3 W which is the power caps.
2. Using the data taken, and with the resistance of AWG # 30 is 0.3451 Ω / m, we can find the maximum distance for the cable. L = 87.3 * 0.5 / 0.3451 = 126.49 m
3. In the question about robosub project, AWG # 28 wire is used with resistance of 0.0764Ω / ft. This particular circuit have nominal rating of 2.6 - 5 V and 20 mA as provided in the question. To determine the maximum length of wire that can be used, we first must calculate the maximum resistance in cable R_cable = 2.4V / 0.02 A = 120 Ω. Once the resistor is calculated, the length of the cable can be determined as L = 120 Ω * 0.5 / 0.0764 Ω/ft = 785 ft.
4. In the next question, we are sending 48 volts at 10A down the sub. 36 volts have to reach the sub and minimum cable gauge has to be determined for a 60 ft tether cable. Since there can only be a 12V drops, the resistance can be figured out to be R = V / I = 12V /10A =1.2Ω. Once the resistor is determined, the cable gauge can be tested and the minimal gauge required for 60 ft tether cable appears to be the AWG#24 since by using it L = 1.2 / 0.0302 = 39.7 ft.

Using a Multimeter

Purpose
      The purpose of this lab is to review on how to correctly use the multimeter to measure current, voltage and resistance in a circuit.

Resistance Test
When the multimeter probe doesn't touch anything, the multimeter reads overload in the multimeter. When the probes is touching each other, it reads 0Ω. After this test is conducted, 4 different resistors are measured its resistance and the result is compiled to this table:

Resistor Colors	Value from Colors	Measured Value	%error
Brown black brown	100Ω	97 ± 0.05 Ω	3.0%
Brown red orange	12000Ω	11.5 ± 0.05 kΩ	4.2%
Orange white yellow	390000Ω	392 ± 0.5 kΩ	0.51%
Red black red	2000Ω	2.02 ± 0.005 kΩ	1.0%

According to the result from the measured value, it actually make sense since the percent error is under five percent which is the tolerance for resistors that have a gold band.

Voltage Test

In this part, a voltage with rating of 12VDC was measured. Since its an unregulated voltage source, a reading of 17.34 V makes sense since it guarantees voltage of 12 V.

Circuit

A circuit consist of a power source, 150 Ω resistor and LED was constructed as follow

The setup of the circuit where the power source positive terminal is connected to the resistor and the negative terminal to the negative side of the diode.

Once the circuit is built, the voltage across the LED and the resistor was measured as shown on the picture below

Probes are set up so it is parallel to the circuit and each elements' voltage drops are measured

The result of the voltage drop is as follow:

    Voltage across resistor = 2.50V

    Voltage across diode = 2.24V

After the voltage was measured, the current was then measured as well. The setup is shown below:

multimeter was set up to measure the current by attaching it in series to the circuit

As seen in the picture, the current is measured to be 26.3 mA.

There is some discrepancy in the value of measured current and the ideal current calculated using Ohm's Law which is the I = V/R. The calculated I appears to be 0.033 A which has 20% error. This error is created because the LED have some resistance that contributes to the error.