SMV ELECTRIC TUTORIALS Nicolo Maganzini, Geronimo Fiilippini, Aditya Kuroodi 2015

RESISTORS IN NETWORKS 2

What are we learning?  Learn about the math behind networks of resistors.  Current and Voltage laws.  Predicting/designing circuits that have specific values of  Current, Voltage, Resistance  Learn about some very important structures of networks  Parallel and series  How are they used?  CAUTION: Math involved. 3

Resistors in Networks 4  In Circuit Schematics:  In Real Life:

Resistor Network Calculations - Series Networks  You have this circuit: R1 = 1 Ohm, R2 = 2 Ohm, R3 = 3 Ohm, V = 6V  How can you apply Ohm’s law to find out how much current is flowing? 5

Series Resistors Equation.  This is called a series connection:  Equivalent Resistance = R1 + R2 + R3 + R4  Since there is only one path for electrons, there is only one current value in the part of the circuit with the series connection.  Try it yourselves! (next slide) 6

The circuit we’re building:  R1 = 100 Ohm  R2 = 220 Ohms  R3 = 300 Ohms  Battery = 9V  Measure current at nodes 1,2. Write them down. Check that they are equal.  Measure voltages V1(across R1), V2 (across R2), V3 (across R3), across the battery.  Calculate:  V1/R1, V2/R2, V3/R3  What should these be equal to?  V1+V2+V3  What should this be equal to?  (V1+V2+V3)/(R1+R2+R3)  What should this be equal to? 7

Parallel Networks  Current has multiple paths it can take.  It will split according to the resistance in each path.  Path with lower resistance gets most current.  Path with higher resistance gets less current.  If resistances are equal, all paths have the same current. 8

Let’s combine the two!  Split circuit between parallel and series parts.  Simplify the parallel part and add it to the series part.  Parallel part simplification:  Overall equation for resistance: 9 This is in Parallel: Find it’s equivalent Then add it to this one!

Sample Problem  Calculate the current flowing out of the battery in this circuit:  R1 = 100 Ohms  R2 = 150 Ohms  R3 = 200 Ohms  Battery = 9V 10

Kirchoff current and voltage laws  How do we analyze more complicated circuits?  There are some physics laws that we can apply to circuits that allows us to find equations: Kirchoff laws.  Steps:  1) Apply Laws  2) Find Equations  3) Solve equations to find current, voltage and resistance. 11

Kirchoff Voltage Law (KVL)  What the law says:  The sum of all voltages in a loop must be equal to zero.  Example of how we use it:  Vbatt = 9V.  V1 = 2V  V2 = 3V  R3 = 4 Ohms  Find the current in the circuit. 12

 Step 1) Apply law:  The voltage produced by the battery is equal to the voltage dropped by each resistor.  Step 2) Find Equation:  Vbatt = V1+V2+V3  Know Vbatt, V1, V2; Find V3  I = V3/R3  Know V3 and R3, Find I.  Step 3) Solve:  V3 = = 4V  I = 4/4 = 1A 13 Kirchoff Voltage Law (KVL)

Kirchoff Current Law (KCL)  What the law says:  The sum of all currents entering and exiting a node must be zero.  Example of how we use it:  R1 = 100 Ohms.  R2 = 200 Ohms  R3 = 200 Ohms.  Current through R1 = 1A  Find voltage of battery. 14

 Step 1) Apply Laws:  Current flowing into node 2 from R2 and R3 must be equal to current flowing out towards R1.  Current flowing in R2 and R3 must be equal because resistances are equal (200 ohm)  Sum of voltages must be equal to the battery voltage  Step 2) equations:  I1 = I2 + I3  I2 = I3  V1+V2 = V1 + V3 = Vbattery  Step 3) solve:  1 = ½ + ½  I2 = I3 = ½ A  V1 = I1 R1 = 100V  V2 = V3 = ½ x 200 = 100V  Vbatt = = 200V 15 Kirchoff Current Law (KCL)

Using series connections to make a sensor 16

CAPACITORS AND SIGNAL FILTERING

What are we learning?  Learning about new components called capacitors.  Learn about how they are different from resistors.  Learn about how capacitors are used in circuits with signals to modify and shape the signal as we want.  Signal filtering with capacitors.  Water analogies

Capacitors store charge  Capacitors in circuits are like water baloons attached to water circuits. Pumpres. reduces flowwater baloon starts Flow filling.  As pump pushes water, baloon fills up and starts pushing backwards, opposing the flow of water more and more.  Water wheel slows down. 19

Charged capacitor  At some point, force of baloon pushing water backwards is equal to force of pump pushing water forward  Assuming weak pump and very strong rubber  No more water flow. Water wheel doesnt turn. Force of pump = Force of baloon Water is still. 20

What if we turn off the pump? 21  Now the pump stops pushing. There is nothing to oppose baloon force, so water flows out of baloon and it starts emptying. The water wheel spins again.  When baloon is empty, water wheel stops and no more water flow.

Now with capacitors.  Circuit analog is RC (resistance-capacitance circuit)  Water wheel is resistor, capacitor is water baloon.  Switch in position 1: current flows from battery, through resistor to capacitor, charges capacitor.  When capacitor is full, force pushing back is equal to force pushing forward, i.e. capacitor and battery are at the same voltage. 22

Capacitor charging  When capacitor is empty,  Force pushing current back is weak: Low voltage  Becomes greater and greater until reaches same voltage as battery.  Amount of current that makes it through is large! (because nothing stops it)  But as capacitor fills up, no more current makes it through. 23

Capacitor Discharging  When battery is disconnected,  Capacitor starts emptying, pushing electrons back out and creating a current.  Initially force is the same as the old battery, but as capacitor is becoming empty, the strength goes down.  Same with current becomes weaker. 24

Large vs. Small capacitors  Capacitance value of capacitor (like resistance for resistors) tells us how large the capacitor is.  What does this mean? Like the size of the baloon. 25 Large or small? Charging Discharging

We also need to take into account the resistance. 26

Ohm’s Law for Capacitors 27

Low Pass Filter

High Pass Filter 29 R = 1 kOhm C = 0.22 microF

What have we learned?  If the signal has a certain frequency, we can make an R-C circuit that cancels the signal out.  If a signal has more than one frequency, such as noise:  Can clean it up using an R-C filter designed to cancel out all frequencies lower than a certain amount. 30