Ch.2. Basic Laws
Part 1 – Kirchhoff’s Laws
Resistance
• 물질의 저항은 단면적(A), 길이( )와 저항계수(resistivity, ρ) 에 의하여 결정
R A
저항의 종류
탄소피막 저항
권선 저항
가변저항
Varistor Thermistor
Ohm ’s Law
• Ohm’s Law : the voltage
v
across a resistor is directly proportional to the currenti
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
Nonlinear Resistor
• Linear & Non-Linear Resistors
Linear resistor Non-Linear resistor
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
G R v
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
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
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)
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
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.
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 andi n
is then
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
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
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 andv m
is the voltage of them
th branch- (Sum of voltage drops) = (Sum of voltage rises)
- Convention: loop current의 방향이 element의 (+)단자
1
0
M
m m
v
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