Circuit Elements; Ohm's Law; KCL;KVL


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Circuit Elements; Ohm's Law; KCL;KVL: 


Basic Electrical Quantities: 

Basic quantities: current, voltage and power Current : time rate of change of electric charge I = dq / dt 1 Amp = 1 Coulomb/sec Voltage : electromotive force or potential, V 1 Volt = 1 Joule/Coulomb = 1 N ·m/coulomb Power : P = I V 1 Watt = 1 Volt · Amp = 1 Joule/sec Basic Electrical Quantities

Current, I: 

Normally we talk about the movement of positive charges although we know that, in general, in metallic conductors current results from electron motion (conventionally positive flow) The sign of the current indicates the direction of flow Types of current: direct current (dc): batteries and some special generators alternating current (ac): household current which varies with time Current, I I( t )

Voltage, V: 

Voltage is the difference in energy level of a unit charge located at each of two points in a circuit, and therefore, represents the energy required to move the unit charge from one point to the other Voltage, V Circuit Element(s) + – V(t)

Default Sign Convention: 

Passive sign convention : current should enter the positive voltage terminal Consequence for P = I V Positive (+) Power: element absorbs power Negative (-) Power: element supplies power Default Sign Convention Circuit Element + – I

Electrical Analogies (Physical): 

Electrical Analogies (Physical)

Active vs. Passive Elements: 

Active elements can generate energy Voltage and current sources Batteries Passive elements cannot generate energy Resistors Capacitors and Inductors (but CAN store energy) Active vs. Passive Elements

Independent Sources: 

An independent source (voltage or current) may be DC (constant) or time-varying (AC), but does not depend on other voltages or currents in the circuit Independent Sources + – Voltage Source Current Source


A resistor is a circuit element that dissipates electrical energy (usually as heat) Real-world devices that are modeled by resistors: incandescent light bulbs, heating elements (stoves, heaters, etc.), long wires Resistance is measured in Ohms ( Ω ) Resistors

Ohm’s Law: 

v(t) = i(t) R - or - V = I R p(t) = i 2 (t) R = v 2 (t)/R [+ (absorbing)] Ohm’s Law v ( t ) The Rest of the Circuit R i ( t ) + –

Open Circuit: 

What if R =  ? i(t) = v(t)/R = 0 Open Circuit v ( t ) The Rest of the Circuit i ( t )=0 + – i ( t )=0

Short Circuit: 

What if R = 0 ? v(t) = R i(t) = 0 Short Circuit The Rest of the Circuit v ( t )=0 i ( t ) + –


Two elements are in series if the current that flows through one must also flow through the other. Series R 1 R 2 Series R 1 R 2 Not Series


Two elements are in parallel if they are connected between (share) the same two (distinct) end nodes. Parallel Parallel Not Parallel R 1 R 2 R 1 R 2

Kirchhoff’s Laws: 

Kirchhoff’s Current Law (KCL) sum of all currents entering a node is zero sum of currents entering node is equal to sum of currents leaving node Kirchhoff’s Voltage Law (KVL) sum of voltages around any loop in a circuit is zero Kirchhoff’s Laws

KCL (Kirchhoff’s Current Law): 

The sum of currents entering the node is zero: Analogy : mass flow at pipe junction KCL (Kirchhoff’s Current Law) i 1 ( t ) i 2 ( t ) i 4 ( t ) i 5 ( t ) i 3 ( t )

KVL (Kirchhoff’s Voltage Law): 

The sum of voltages around a loop is zero: Analogy : pressure drop thru pipe loop KVL (Kirchhoff’s Voltage Law) v 1 ( t ) + + – – v 2 ( t ) v 3 ( t ) + –