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Kirchoffs Current Law (KCL)

The sum of the currents entering a node is

equal to the sum of the current leaving the

node.

The algebraic sum of currents entering a

node (or a closed boundary) is zero

!

!N

n

ni

1

0

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Kirchoffs Current Law (KCL)

We know the currentI1 = 2 A. What iscurrent I2?

I1 = I2 = 2A

This confirms for us

that two elements inseries must have thesame current

I1

I2

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Kirchoffs Current Law (KCL)

Find the current I0

in the following circuit.

AIAA

IIoutin

10420!

!

I0

4 A

10 A

2 A

I

I

4

1042

0

0

!

!

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Kirchoffs Current Law (KCL)

There are two ways to

find I:

Find Req and then

calculate I

Find I1 and I2 and

then calculate I

I

I2I1

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Kirchoffs Current Law (KCL)

Find Req and then

calculate I

Req = 10/2 = 5

I = 10/5 = 2A

I

I2I1

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Kirchoffs Current Law (KCL)

Find I1 and I2 and

then calculate I

I1 = 10/10 = 1A

I2 = 10/10 = 1 A

I = I1 + I2 = 2 A

I

I2I1

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Kirchoffs Voltage Law (KVL)

The algebraic sum of all voltages around a

closed path (or loop) is zero

Sum of voltage drops = Sum of voltage

rises

!

!M

m

mv

1

0

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Circuit Definitions

In Series, voltage sources add

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Circuit Definitions

In Parallel, voltage sources provide more

current but have the same voltage

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Review Question 2.9

Which of the circuits below will give you Vab

= 7V?

a) b)

c) d)

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Resistors in Series

The equivalent resistance of any number

of resistors connected in series is the sum

of the individual resistances.

Neq RRRR ! -21

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Resistors in Parallel

The equivalent resistance of any number

of resistors connected in parallel is the

reciprocal of the sum of the reciprocals

Neq RRRR

1111

21

! -

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Resistors in Parallel

The equivalent resistance of any two

resistors in parallel can be expressed

more simply as:

21

21

RRRRReq

!

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Voltage Division

To calculate the voltage drop across each

resistor, use the following equations:

SV

RR

RV

21

1

1

!

SV

RR

RV

21

2

2

!

VS

R1

R2

+ V1_

+

V2_

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Current Division

To calculate the current going through each

resistor, use the following equations:

SI

RR

RI

21

2

1

!

SI

RR

RI

21

1

2

!

IS R1 R2I1 I2