Tuesday week 11, lect 19
Calculate voltage and current using Ohms Law.
BatteryResistor
V=10V 
R =100W 
I=0.1A=100mA 
V=5V 
R=22 W 
I=0.23 =230 mA 
V=9V 
R= 30000 W 
I=0.0003 A =300 mA 
You should be able to calculate any one given the other two.
Students will be responsible for powers of 10 in the units.
milli m 1/1000 3mA =.003A
mega M 1,000,000 10MW= 10,000,000 W
micro m 1/1000000 100mV=0.0001 V
Battery – 2 resistors in series
V=10V [5V,5V] 
R1 =50W R2=50W 
I=0.1A=100mA 
V=5V [0.24V, 4.76V] 
R1=22 W R2=432 
I=0.01 =10 mA 
V=9V [8.9997V, 0.000299V]] 
R1= 30000 W R2=1W 
I=0.0003 A =299 mA 
You must realize that the current through each resistor is the same and that the sum of the voltages along the path of resistors in series is the applied voltage.
For a string of resistors in series the current through the circuit is calculated by treating the circuit as a single resistor equal to the sum of the actual resistors. Once you have the current the individual voltages across each resistor can be found by multiplying the current and the individual resistance,
Battery parallel
V 
W 
A 
9 
30000 
3.00E04 
9 
22 
4.09E01 
9 
678 
1.33E02 
9 
1024 
8.79E03 
Use kW, mA for some of these results.
Multiple (2 batteries in series3R2R) [9V+9V=18V]
V 
W 
W 
W 
I 
18 
22 
432 
0 
3.96E02 
V= 
0.872246696 
17.1277533 
0.00E+00 
18 
V 
W 
W 
W 
I 
18 
50 
100 
200 
5.14E02 
V= 
2.571428571 
5.142857143 
1.03E+01 
18 
AC voltages & currents
More complicated circuits involve PS that have changing voltages. In our homes the voltage alternates. It changes from 120V to 120V in a smooth continuous way that is referred to as sinusoidal variation. This is the same behavior that pure notes behave. If you view the pressure vs time for a sound wave from a tuning fork you will see the same type of function.
The circuits above are a bit more complicated to analyze but the voltage, current and resistance are still linked by OhmÕs law. So you simply evaluate current and voltage at the same time (keep resistance as fixed in time).
Having introduced time dependent voltages and currents we should recognize that phenomena out side of electrical system could be converted into voltages and/or currents for analysis. We will restrict ourselves to transducers that convert data into voltages.
sound 
Pressure vs time 
microphone 
distance 
Moving object 
Sonic ranger 
Power 
Motor doing work 
Power meter 
Light intensity 


color 


loudness 


speed 


É 


ADC analog to digital converter converts a voltage vs time to a number vs time.
To be clear we have been plotting the data as if we knew the numerical value of the voltage. An ADC simply performs that function so that numerical data are actually input into a computer. In principle we know that all voltages have numerical values. The ADC just does the actual translation in a system with a transducer.
To really understand this process we need to distinguish digital and analog signals. A digital signal breaks the continuous values that we imagine are present in the voltage versus time plots and breaks the continuous variation into a series of discrete steps.
The simplest digital system is the two step or two state system.
1 
True 
On 
TTL=5V 
Hand raised 
0 
False 
Off 
TTl=0V 
Hand down 
With only two possible outcomes the analysis of these two states falls to the area of logic. We use this in our everyday lives. There is class [TRUE] or there is no class [FALSE]. I am going/not to bed. Weather is good/bad. Based on these two state situations we make decisions. Do I play soccer? [yes/no]. Do I watch TV [Y/N]? To implement the mathematics of T/F we introduce the operations and & or. We can also negate i.e. turn a true into a false and vice versa. With all the statements above we can make our relationships more complicated. It is possible to introduce entities into a decision making process that require more than two states. When the situation only employs Y/N as the values then we are dealing with digital logic. In examining problems you need to be able to reduce all of the situations of importance two one of two possible states. The classic example of a digital system for me is a street light. The light breaks all the interactions into a go/wait outcome and evaluates each input as present/empty. So are pedestrians waiting or there are not. There are cars heading north or not. Now indeed should there be a patrolman directing traffic he can introduce more complex states. Rather that simply letting cars gogreen or stopred. He can instruct cars to go quickly or have them go slowly. This then has 3 states quick, slow, stop. The clever student might realize that I could still reduce the problem to a logic problem by letting the states be go/stop but introduce two ways to go [fast, slow]. Indeed computers of today are primarily using twostate digital logic and the problems are formulated or broken down into a complex system of logic.
Let us consider another example of a problem that is typically described as a digital process. The music we hear is treated as analog. There is a continuous transition from soft to loud. Hills and valleys were made in plastic (records) so that sound systems could reproduce this recorded music. This was analog there was no prescribed depth or height the groves had hills and valleys of arbitrary heights and the path along the groove was continuous. Engineers then developed ways to record numbers & methods to digitize recorded sound. To digitize music one picks a step size in time and a step size in loudness. As the music progresses you analyze the sound that falls in one time step and assign it a value in terms of loudness steps. Time progresses as 0,1,2,3,4,5,6É. Each interval is represented as an integer and there are no decimal values. They have been eliminated. There is no sound value for 1.5 but there is a value for 1 and 2. Thus any song can be represented as a string of numbers.
time 
amplitude 
0 
134 
1 
157 
2 
126 
3 
122 
Information in this format can be stored and manipulated in a computer. The ADC that we began talking about can translate analog information such as sound into a stream of numbers.
The understanding of digital signals and there relationship to analog signals is critical for robotics. Many sensors incorporated simply translate information into electrical signals that is then processed into numbers. For some implementations a basic digital on/off approach suffices [motor: forward or reverse] for others broader digital approach [motor: speed].