Lecture8

Review

Kirchhoff’s Laws

Voltage and Current Division

CS 21 - Computer Organization and Assembly Language Programming Lecture 8 Introduction to Electrical Devices and Circuits 2 University of the Philippines - Diliman College of Engineering Department of Computer Science

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Kirchhoff’s Laws

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Kirchhoff’s Laws

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Voltage and Current Division

Voltage and Current Division

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Kirchhoff’s Laws

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Kirchhoff’s Laws

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Voltage and Current Division

Voltage and Current Division

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Kirchhoff’s Laws

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Charge Current Voltage Resistance Power

Voltage and Current Division

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Kirchhoff’s Laws

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Charge - positive or negative (C)

Voltage and Current Division

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Kirchhoff’s Laws

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Charge - positive or negative (C) Current - flow of charges (A)

Voltage and Current Division

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Kirchhoff’s Laws

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Charge - positive or negative (C) Current - flow of charges (A) Voltage - energy required to ”push charges” (V)

Voltage and Current Division

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Kirchhoff’s Laws

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Charge - positive or negative (C) Current - flow of charges (A) Voltage - energy required to ”push charges” (V) Resistance - opposition to current (Ω)

Voltage and Current Division

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Kirchhoff’s Laws

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Charge - positive or negative (C) Current - flow of charges (A) Voltage - energy required to ”push charges” (V) Resistance - opposition to current (Ω) Power - rate at which energy is expended (W)

Voltage and Current Division

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Kirchhoff’s Laws

More Review

Ohm’s Law Series Parallel

Voltage and Current Division

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Kirchhoff’s Laws

More Review Ohm’s Law: V = IR

Voltage and Current Division

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Kirchhoff’s Laws

More Review Ohm’s Law: V = IR Series: same current

Voltage and Current Division

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Kirchhoff’s Laws

More Review Ohm’s Law: V = IR Series: same current Parallel: same voltage

Voltage and Current Division

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Kirchhoff’s Laws

More Review Ohm’s Law: V = IR Series: same current Parallel: same voltage

Voltage and Current Division

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Kirchhoff’s Laws

Outline

1

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Kirchhoff’s Laws

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Voltage and Current Division

Voltage and Current Division

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Kirchhoff’s Laws

Voltage and Current Division

Kirchhoff’s Current Law Principle of Conservation of Mass The net sum of the currents entering any node is zero

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Kirchhoff’s Laws

Voltage and Current Division

Kirchhoff’s Current Law Principle of Conservation of Mass The net sum of the currents entering any node is zero

Path of least resistance: there is larger current in the path that has lower resistance

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Kirchhoff’s Laws

Kirchhoff’s Current Law Example

Find the current through RA

Voltage and Current Division

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Kirchhoff’s Laws

Voltage and Current Division

Kirchhoff’s Current Law Example

Find the current through RA

We first compute for the current through the 20Ω resistor

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Kirchhoff’s Laws

Voltage and Current Division

Kirchhoff’s Current Law Example

Find the current through RA

We first compute for the current through the 20Ω resistor Using Ohm’s Law, I = V/R = 40/20 = 2A

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Kirchhoff’s Laws

Kirchhoff’s Current Law Example

Simplifying the circuit, we have

Voltage and Current Division

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Kirchhoff’s Laws

Kirchhoff’s Current Law Example

Simplifying the circuit, we have

Using KCL, 2A + IA = 5A + 22A

Voltage and Current Division

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Kirchhoff’s Laws

Voltage and Current Division

Kirchhoff’s Current Law Example

Simplifying the circuit, we have

Using KCL, 2A + IA = 5A + 22A

—>

IA = 25A

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Kirchhoff’s Laws

Voltage and Current Division

Kirchhoff’s Voltage Law

Principle of Conservation of Energy The net sum of voltages around any closed path is zero

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Kirchhoff’s Laws

Kirchhoff’s Voltage Law Example Find vx .

Voltage and Current Division

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Kirchhoff’s Laws

Voltage and Current Division

Kirchhoff’s Voltage Law Example Find vx .

First, let’s assign the positive-negative sides on the circuit elements.

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Kirchhoff’s Laws

Voltage and Current Division

Kirchhoff’s Voltage Law Example Find vx .

First, let’s assign the positive-negative sides on the circuit elements.

Review

Kirchhoff’s Laws

Kirchhoff’s Voltage Law Example Find vx .

Ohm’s Law at 8Ω resistor: V8 = IR = 2A*8Ω = 16V

Voltage and Current Division

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Kirchhoff’s Laws

Kirchhoff’s Voltage Law Example Find vx .

Ohm’s Law at 8Ω resistor: V8 = IR = 2A*8Ω = 16V KVL at first loop (first box): -30 + 16 + V10 = 0 V10 = 14V I10 = V10 /R = 14V/10Ω = 1.4A

Voltage and Current Division

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Kirchhoff’s Laws

Kirchhoff’s Voltage Law Example Find vx .

KCL at the node: 2 = 1.4 + I2a —>

I2a = 0.6A

Voltage and Current Division

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Kirchhoff’s Laws

Kirchhoff’s Voltage Law Example Find vx .

KCL at the node: 2 = 1.4 + I2a —>

I2a = 0.6A

Ohm’s Law at R2a (2Ω resistor at top): V2a = I2a *R2a = 0.6A*2Ω = 1.2V

Voltage and Current Division

Review

Kirchhoff’s Laws

Voltage and Current Division

Kirchhoff’s Voltage Law Example Find vx .

KCL at the node: 2 = 1.4 + I2a —>

I2a = 0.6A

Ohm’s Law at R2a (2Ω resistor at top): V2a = I2a *R2a = 0.6A*2Ω = 1.2V KVL at second loop: -14 + 1.2 + V2b = 0

—>

V2b = 12.8V

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Kirchhoff’s Laws

Voltage and Current Division

Kirchhoff’s Voltage Law Example Find vx .

KCL at the node: 2 = 1.4 + I2a —>

I2a = 0.6A

Ohm’s Law at R2a (2Ω resistor at top): V2a = I2a *R2a = 0.6A*2Ω = 1.2V KVL at second loop: -14 + 1.2 + V2b = 0

—>

V2b = 12.8V = vx

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Kirchhoff’s Laws

Outline

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Kirchhoff’s Laws

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Voltage and Current Division

Voltage and Current Division

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Kirchhoff’s Laws

Voltage and Current Division

Voltage Division Used to express the voltage across one of several series resistors in terms of the voltage across the platform

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Kirchhoff’s Laws

Voltage and Current Division

Voltage Division

Since the circuit is in series, current is constant

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Kirchhoff’s Laws

Voltage Division

Therefore, the current is:

Voltage and Current Division

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Kirchhoff’s Laws

Voltage Division

Solving for the voltage in Resistor 2:

Voltage and Current Division

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Kirchhoff’s Laws

Voltage Division

And for Resistor 1:

Voltage and Current Division

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Kirchhoff’s Laws

Voltage Division

In general:

Voltage and Current Division

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Kirchhoff’s Laws

Voltage Division Example

Find vx using voltage division.

Voltage and Current Division

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Kirchhoff’s Laws

Voltage Division Example

Find vx using voltage division.

First, simplify the circuit Use resistor equivalence for parallel resistors

Voltage and Current Division

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Kirchhoff’s Laws

Voltage Division Example

Find vx using voltage division.

Voltage and Current Division

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Kirchhoff’s Laws

Voltage and Current Division

Voltage Division Example

Find vx using voltage division.

Then solve for vx using the voltage division formula vx = v (Rx / ÎŁR )

Review

Kirchhoff’s Laws

Voltage and Current Division

Voltage Division Example

Find vx using voltage division.

Then solve for vx using the voltage division formula vx = v (Rx / ΣR ) = 10V (2Ω / 10Ω)

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Kirchhoff’s Laws

Voltage and Current Division

Voltage Division Example

Find vx using voltage division.

Then solve for vx using the voltage division formula vx = v (Rx / ΣR ) = 10V (2Ω / 10Ω) = 2V

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Kirchhoff’s Laws

Voltage and Current Division

Current Division

For parallel resistors, we use current division instead

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Kirchhoff’s Laws

Voltage and Current Division

Current Division

Remember that voltage is constant in parallel connections

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Kirchhoff’s Laws

Voltage and Current Division

Current Division

Using Ohm’s law and Resistor Equivalence:

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Kirchhoff’s Laws

Voltage and Current Division

Current Division

Therefore, the current passing through Resistor 2 is:

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Kirchhoff’s Laws

Voltage and Current Division

Current Division

And the current passing through Resistor 1 is:

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Kirchhoff’s Laws

Current Division

In general:

Voltage and Current Division

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Kirchhoff’s Laws

Current Division Example

Find V5 .

Voltage and Current Division

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Kirchhoff’s Laws

Voltage and Current Division

Volt Sources - Series Just like resistors, volt sources can be reduced to one equivalent source as well.

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Kirchhoff’s Laws

Voltage and Current Division

Volt Sources - Series Just like resistors, volt sources can be reduced to one equivalent source as well.

Volt sources in series can be summed up into one.

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Kirchhoff’s Laws

Voltage and Current Division

Volt Sources - Series Just like resistors, volt sources can be reduced to one equivalent source as well.

Volt sources in series can be summed up into one.

Consider

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Kirchhoff’s Laws

Voltage and Current Division

Volt Sources - Series Just like resistors, volt sources can be reduced to one equivalent source as well.

Volt sources in series can be summed up into one.

We can add all the volt sources in series (as well as the resistors)

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Kirchhoff’s Laws

Current Sources - Parallel

We can also reduce current sources.

But they must be in parallel connection instead.

Voltage and Current Division

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Kirchhoff’s Laws

Voltage and Current Division

Seatwork: Network Analysis Given that a,b,c = 1Ω, d,e,f,g,h,i = 3Ω and j,k,l = 5Ω And suppose the 30V source supplies 12A Find the following: Va , Vf , Vk , Ib , Ie and Il Find the equivalent resistor as well

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Kirchhoff’s Laws

So...

Any questions?

Voltage and Current Division