1

Electric ChargeOne of the seven fundamental SI units.

Circuit analysis involves determining the current flowing through and the voltage present across circuit elements.

Current and voltage are both based on electric charge.

2

Electric Charge

In the early 1900s, scientists began to identify the particles that make up atoms (subatomic particles).

They identified the proton, the neutron, and the electron.

3

Electric Charge

Protons (positive charge) and neutrons (neutral or no charge) are bound in the nucleus and do not affect electrical behavior.

4

Electric Charge

Electrons (negative charge) surround the nucleus occupying specific energy states. Their exact position is unknown, but their energy level is precisely known.

5

Electric Charge

When an electron is removed from its atomic orbital, it becomes a free electron. The flow of free electrons (negative charges) or the “flow” of the “holes” left in the orbitals after the electrons leave (positive charges) constitute an electric current.

6

Electric ChargeCharge is responsible for electrical forces.

Charge must be conserved – it cannot be created or destroyed.

Charge is measured in coulombs (C) and is abbreviated “q”.

The charge of one electron is –1.602 10-19 C.

–1 C equals the charge of 6.24 1018 electrons.

7

CurrentElectric current is the flow of electric charge.

Current is measures in amperes (A) and is abbreviated with the symbol “I ” or “i ”.

“Amperes” is often shortened to “amps”.

NOTE: A meter that measures current is called an “ammeter” – NOT an “ampmeter”!

dt

)t(dq)t(i

f

i

dt)t(i)t(q1 A = 1 C/s

where t0 is some initial time at which the charge is known.

Current

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VoltageVoltage is the difference in electric potential between two points.

Voltage provides an electromotive force – a force that moves charge carriers through a circuit.

Voltage is measured in volts (V) and is abbreviated with the symbol “V” or “v” (or sometimes “E” ).

NOTE: A meter that measures voltage IS called an “voltmeter”!

One joule of energy is needed to move one coulomb of charge through a potential difference of one volt.

1 V = 1 J/C (1 J = 1 kg-m2/s2)

Voltages can be constant with time or they can vary.Constant Voltage : DC voltages

Varying Voltage in time and magnitude: AC voltages

V(t) = 10 V

V(t) = 10 cos (200πt)

-

+

VI

I

V

V

I

ωt0 π/2 π 2π 3π 4π

VM

VMsinωt

VMcosωt

Voltage

Basic Circuit Elements• Sources (voltage and current)

– Independent sources– Dependent sources

• Resistors

• Capacitors

• Inductors

CIRCUIT COMPONENTS• Branch:• a single path in a circuit composed of one

simple element and the nodes at either end of the element

• Node:• a point at which two or more elements have a

common connection• Supernode:• a closed surface containing several nodes• Mesh:• a loop that does not enclose another loop• Supermesh:• a closed path around adjacent meshes that

share a current source• Closed path (or a loop):• a closed path through circuit components i1 v

1v4

v3

v5

v6

i2

i3 i4

i6i7

v2

Simple Circuit Laws

• Ohm’s Law

• Kirchhoff’s Current Law (KCL)

• Kirchhoff’s Voltage Law (KVL)

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Ohm’s Law

Interpretation (DC circuit): The voltage across a circuit element is directly proportional to the current through the element. The proportionality constant is called the “resistance” of the circuit element.

Shows a linear relationship between voltage and current.

Linear Relationship: V = R I ↔ y = mx + b

V = IR, where V=voltage, I=current, and R=resistance

•The two extreme values a resistor can take are zero (short-circuit) and infinity (open-circuit):•SHORT CIRCUIT: defined as a “zero resistance element”; i.e. an ideal wire.•OPEN CIRCUIT:defined as an “infinite resistance element”; or an “open” path in a circuit.

•In a basic circuit all wires will be assumed to have zero resistance. In practical applications, the resistance of wires may have to be taken into account.

•Real resistors have certain limitations; the most common one is a “power” rating: i.e. resistors can only support a certain amount of electrical power (vi) before failing.

vR

+ -

iR

R vR

+ -

iR

R

Ohm’s Law

MEASURING V & I• Voltage is measured ACROSS a device; the probes of a voltmeter

are attached at both ends of the device under test or in parallel with device.

• Current is measured THROUGH a device; the ammeter must be connected in series with the device

What is the current, I?

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Gustav Kirchhoff

Kirchhoff’s Current Law (KCL)

The sum of the currents entering a node equals the sum of the currents exiting that node.

Node: A closed path enclosing part of a circuit.

A violation of KCL violates the Law of Conservation of Charge (or Mass)!

In other words: Whatever goes in must come out.

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Gustav Kirchhoff

Kirchhoff’s Voltage Law (KVL)

The sum of the voltage rises around any closed path in a circuit equals the sum of the voltage drops around that path.

A violation of KVL violates the Law of Conservation of Energy!

In other words: When you make a round trip, you end up where you started.

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Series and ParallelTwo or more circuit elements in series carry the same current.

Two or more circuit elements in parallel have the same voltage across them.

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Series and Parallel

Series: Two or more circuit elements carry same current.

Parallel: Two or more circuit elements have the same voltage across them.

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Applications of KCL

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Applications of KVL