Electric Charge One 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.

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.

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

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

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.

Electric Charge Charge 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.

Current Electric 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”! 1 A = 1 C/s

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

Voltage Voltage 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)

Voltage V(t) = 10 V V(t) = 10 cos (200πt) Voltage 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)

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

Simple Circuit Laws Ohm’s Law Kirchhoff’s Current Law (KCL) Kirchhoff’s Voltage Law (KVL)

Ohm’s Law V = IR, where V=voltage, I=current, and R=resistance Shows a linear relationship between voltage and current. V = IR, where V=voltage, I=current, and R=resistance 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. Linear Relationship: V = R I ↔ y = mx + b

Ohm’s Law 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.

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?

Gustav Kirchhoff Node: A closed path enclosing part of a circuit. Kirchhoff’s Current Law (KCL) A violation of KCL violates the Law of Conservation of Charge (or Mass)! The sum of the currents entering a node equals the sum of the currents exiting that node. In other words: Whatever goes in must come out.

Gustav Kirchhoff A violation of KVL violates the Law of Conservation of Energy! Kirchhoff’s Voltage Law (KVL) In other words: When you make a round trip, you end up where you started. The sum of the voltage rises around any closed path in a circuit equals the sum of the voltage drops around that path.

Series and Parallel Two or more circuit elements in series carry the same current. Two or more circuit elements in parallel have the same voltage across them.

Series and Parallel Series: Two or more circuit elements carry same current. Parallel: Two or more circuit elements have the same voltage across them.

Applications of KCL

Applications of KVL