Lecture 2Basic Circuit Laws

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Basic Circuit Laws2.1 Ohm’s Law.

2.2 Nodes, Branches, and Loops.

2.3 Kirchhoff’s Laws.

2.4 Series Resistors and Voltage Division.

2.5 Parallel Resistors and Current Division.

2.6 Wye-Delta Transformations.

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2.1 Ohms Law (1)• Ohm’s law states that the voltage across

a resistor V(v) is directly proportional to the current I(A) flowing through the resistor.

• When R=0 short circuit• When R= open circuit.

IR

IRV

R

R

IV

VVV

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ab

baab

Resistance

alityproportion ofconstant

a

b

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2.1 Ohms Law (2)• Conductance is the ability of an element to

conduct electric current; it is the reciprocal of resistance R and is measured in siemens.

• The power dissipated by a resistor:

v

i

RG

1

R

vRivip

22

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2.4 Series Resistors and Voltage Division (1)

• Series: Two or more elements are in series if they are cascaded or connected sequentially and consequently carry the same current.

• The equivalent resistance of any number of resistors connected in a series is the sum of the individual resistances.

• The voltage divider can be expressed as

N

nnNeq RRRRR

121

vRRR

Rv

N

nn

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321)(

VVVV

IIII

Totalseries

Totalseries

As the current goes through the circuit, the charges must USE ENERGY to get through the resistor. So each individual resistor will get its own individual potential voltage). We call this voltage drop.

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series

seriesTT

Totalseries

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RRRR

RIRIRIRI

IRVVVVV

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;Note: They may use the terms “effective” or “equivalent” to mean TOTAL!

2.4 Series Resistors and Voltage Division (1)

ExampleA series circuit is shown to the left. a) What is the total resistance?

b) What is the total current?

c) What is the current across EACH resistor?  

d) What is the voltage drop across each resistor?( Apply Ohm's law to each resistor separately)

R(series) = 1 + 2 + 3 = 6W

DV=IR 12=I(6) I = 2A

They EACH get 2 amps!

V1W=(2)(1)= 2 V V3W=(2)(3)= 6V V2W=(2)(2)= 4V

Notice that the individual VOLTAGE DROPS add up to the TOTAL!!

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2.5 Parallel Resistors and Current Division (1)

• Parallel: Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them.

• The equivalent resistance of a circuit with N resistors in parallel is:

• The total current i is shared by the resistors in inverse proportion to their resistances. The current divider can be expressed as:

Neq RRRR

1111

21

n

eq

nn R

iR

R

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2.5 Parallel Resistors and Current Division (1)• Parallel wiring means that the devices are connected in such a way

that the same voltage is applied across each device.

• Multiple paths are present.• When two resistors are connected in parallel, each receives current

from the battery as if the other was not present.• Therefore the two resistors connected in parallel draw more current

than does either resistor alone.

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321

321

321

1111

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V

R

V

R

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Example 4

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To the left is an example of a parallel circuit. a) What is the total resistance?  

b) What is the total current?  

c) What is the voltage across EACH resistor?   d) What is the current drop across each resistor? (Apply Ohm's law to each resistor separately)

2.20 W

3.64 A

8 V each!

9

8

7

8

5

8975 III

IRV

1.6 A 1.14 A 0.90 A

Notice that the individual currents ADD to the total.

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KIRCHHOFF'S RULES

Gustav Kirchhoff1824-1887

German Physicist

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2.2 Nodes, Branches and Loops (1)

A branch represents a single element such as a

voltage source or a resistor.

A node is the point of connection between two

or more branches.

A loop is any closed path in a circuit.

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2.2 Nodes, Branches and Loops (2)

Example 1

How many branches, nodes and loops are there?

4 Branches

3 Nodes

4 loops

Original circuitEquivalent circuit

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2.2 Nodes, Branches and Loops (3)Example 2 Should we consider it as one

branch or two branches?

How many branches, nodes and loops are there?

7 Branches

4 Nodes

4 loops

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2.3 Kirchhoff’s Laws (1)

Kirchhoff’s current law (KCL) states that the algebraic sum of currents entering a node (or a closed boundary) is zero.

01

N

nni

Mathematically,

Junction Rule

Conservation of mass Electrons entering must

equal the electrons leaving The junction rule states

that the total current directed into a junction must equal the total current directed out of the junction.

Kirchhoff’s Current Law

At any instant the algebraic sum of the currents flowing into any junction in a circuit is zero

For example I1 – I2 – I3 = 0

I2 = I1 – I3

= 10 – 3

= 7 A

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2.3 Kirchhoff’s Laws (3) Kirchhoff’s voltage law (KVL) states that the algebraic

sum of all voltages around a closed path (or loop) is zero.

Mathematically, 01

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Kirchhoff’s Voltage Law

At any instant the algebraic sum of the voltages around any loop in a circuit is zero

For example

E – V1 – V2 = 0

V1 = E – V2

= 12 – 7

= 5 V

Example 14 Using Kirchhoff’s Loop Rule

Determine the current in the circuit.

drops potentialrises potential

0.8V 0.6 12V 24 II

A 90.0

I 20 V 18

I

i

iV 0

321 VVVVbattery

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2.3 Kirchhoff’s Laws (4)Example 5

Applying the KVL equation for the circuit of the figure below.

Va-V1-Vb-V2-V3 = 0

V1 = IR1 V2 = IR2 V3 = IR3

Þ Va-Vb = I(R1 + R2 + R3)

321 RRR

VVI ba

Loop Rule The loop rule expresses conservation of

energy in terms of the electric potential. States that for a closed circuit loop, the total

of all potential rises is the same as the total of all potential drops.