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Ch.2. Basic Laws Part 1 – Kirchhoff’s Laws

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Ch.2. Basic Laws

Part 1 – Kirchhoff’s Laws

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Resistance

• 물질의 저항은 단면적(A), 길이( )와 저항계수(resistivity, ρ) 에 의하여 결정

R   A

(4)

저항의 종류

탄소피막 저항

권선 저항

가변저항

Varistor Thermistor

(5)

Ohm ’s Law

• Ohm’s Law : the voltage

v

across a resistor is directly proportional to the current

i

flowing through the resistor.

• Unit : 1Ω = 1 V/A

• short & open circuits

-Short : a circuit element with resistance approaching zero -Open : a circuit element with resistance approaching infinity

or v v iR R

  i

(6)

Nonlinear Resistor

• Linear & Non-Linear Resistors

Linear resistor Non-Linear resistor

(7)

Conductance

• Conductance

G

: the reciprocal of resistance or the ability of an element to conduct electric current

• Unit : 1 ℧ = 1/ Ω=1A/V

1 i

GRv

(8)

Network Topology : Branch & Node

• Branch : a single element such as a source or a resistor

• Node : the point of connection between two or more branches. If a short circuit connects two nodes, the two nodes are considered as one node

(9)

Network Topology : Loop

• Loop : Any closed path in a circuit

• Independent loop : a loop contains a branch which is not included in any other loop. “The independent loops result in independent sets of equations.”

• # of independent loops

Independent Loops = Branch – Node + 1

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Network Topology : 직병렬 연결

• 직렬연결(series connection) : two or more elements are in

series

if they are cascaded or connected sequentially and consequently carry the same current

(두 개 이상의 branch가 하나의 노드만을 공유하고 있고 다른 branch가 그 노드에 연결되어 있지 않는 경우)

• 병렬연결(parallel connection) : two or more elements are in

parallel

if they are connected to the same nodes and consequently have the same voltage across them

(두개 이상의 branch가 두개의 노드를 공유하고 있는 경 우)

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Network Topology : 직병렬 연결

• 직렬연결(series connection) : two or more elements are in

series

if they are cascaded or connected sequentially and consequently carry the same current

(두 개 이상의 branch가 하나의 노드만을 공유하고 있고 다른 branch가 그 노드에 연결되어 있지 않는 경우)

• 병렬연결(parallel connection) : two or more elements are in

parallel

if they are connected to the same nodes and consequently have the same voltage across them

(두개 이상의 branch가 두개의 노드를 공유하고 있는 경

(12)

Network Topology : 직병렬 연결

Example 2.4

Determine the number of branches and nodes.

Identify which elements are in series and which are in parallel.

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Kirchhoff ’s Current Law

• Kirchhoff’s Current Law (KCL) ; “conservation of charge”

- the algebraic sum of currents entering a node (or a closed boundary) is zero :

where

N

is the number of branches connected to the node and

i n

is the

n

th current entering the node

- the sum of the currents entering a node is equal to the sum of the currents leaving the node

1

0

N n n

i

 

(14)

Kirchhoff ’s Current Law

• Examples of KCL

1 3 4 2 5

i     i i i i

1 2 3 4 5

i     i i i i

  

Current sources in parallel

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Kirchhoff ’s Voltage Law

• Kirchhoff’s Voltage Law (KVL) ; “conservation of energy”

- the algebraic sum of voltages around a closed path (or loop) is zero :

where

M

is the number of branches in the loop and

v m

is the voltage of the

m

th branch

- (Sum of voltage drops) = (Sum of voltage rises)

- Convention: loop current의 방향이 element의 (+)단자

1

0

M

m m

v

 

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Kirchhoff ’s Voltage Law

• Examples of KVL

1 2 3 4 5

0

v v v v v

     

2 3 5 1 4

v     v v v v

Voltage sources in series

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Kirchhoff ’s Laws

Example 2.5

Find the voltage v

1

and v

2

.

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Kirchhoff ’s Laws

Example 2.6

Determine v

0

and i .

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Kirchhoff ’s Laws

Example 2.7

Find current i

0

and voltage v

0

.

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Kirchhoff ’s Laws

Example 2.8

Find the currents and voltages in the circuit

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