SMV ELECTRIC TUTORIALSNicolo Maganzini, Geronimo Fiilippini, Aditya Kuroodi

2015

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RESISTORS IN NETWORKS

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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.

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Resistors in Networks In Circuit Schematics:

In Real Life:

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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?

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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)

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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?

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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.

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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:

This is in Parallel: Find it’s equivalent

Then add it to this one!

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Sample Problem

Calculate the current flowing out of the battery in this circuit:

R1 = 100 Ohms

R2 = 150 Ohms

R3 = 200 Ohms

Battery = 9V

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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.

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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.

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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 = 9-2-3 = 4V

I = 4/4 = 1A

Kirchoff Voltage Law (KVL)

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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.

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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 = 100 + 100 = 200V

Kirchoff Current Law (KCL)

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Using series connections to make a sensor Potential divider equation:

VERY IMPORTANT EQUATION.

Pseudo-Derivation

If Resistance values are constant, then Vout will be constant.

What if the resistance of one resistor changes with temperature or light? How does Vout change?

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.

Pump res. reduces flow water 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.

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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.

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What if we turn off the pump? 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.

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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.

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Capacitor charging

When capacitor is empty,

Force pushing current back isweak: Low voltage

Becomes greater and greateruntil reaches same voltage asbattery.

Amount of current that makesit through is large! (becausenothing stops it)

But as capacitor fills up, nomore current makes it through.

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Capacitor Discharging

When battery is disconnected,

Capacitor starts emptying,pushing electrons back out and creating a current.

Initially force is the same as theold battery, but as capacitor isbecoming empty, the strengthgoes down.

Same with current becomes weaker.

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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.

Large or small?

Large or small?

Charging

Discharging

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We also need to take into account the resistance. Speed at which capacitor charges depends also on

how much resistance in the circuit

Small resistance = more current = faster charging.

Large resistance = less current = slower charging.

Time constant has both capacitance and resistance

is the time required for voltage or current to change by 63.2%

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Ohm’s Law for Capacitors Voltage across resistor depends on value of current at

that instant in time:

Voltage across capacitor depends on how fast the current is changing:

where = Capacitive

Reactance

V is maximum voltage across capacitor, I is maximum current through capacitor, C is capacitance, f is frequency of signal.

Remember potential divider equation?

Voltage across R2 is given by:

Now substitute R2 with reactance

Can you do it?

Increase resistance = lower

Increase capacitance = lower

Increase frequency = lower

This is a LOW PASS FILTER.

Can tune and to cancel out the right requencies.

Low Pass Filter

𝑉𝑉 𝑜𝑢𝑡

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What if we turn around the circuit, so that capacitor is on the top?

substitute for .

Can you simplify it?

This time low frequencies areattenuated

This is a high pass filter.

Note: if signal has f = 0, it is completely eliminated

DC is blocked. Only signals that change in time make it through

High Pass Filter

𝑅

𝐶

𝑉 𝑉 𝑜𝑢𝑡

R = 1 kOhm C = 0.22 microF

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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.