Chapter 1 Variables and Circuit Elements

SUB TOPICS : Introduction International System of Units, SI Current and Voltage Power and Energy Ideal Basic Circuit Elements Basic Circuit Connections Application of Passive Sign Convention to Ohm’s Law and Power Calculation Ohm’s Laws Kirchhoff’s Laws

Introduction There are several ways of describing or defining electric circuit: Definition 1: Electric circuit is a mathematical model that approximates the behavior of an actual electrical system. Hence the analysis of a circuit is a study of the behavior of the circuits. Definition 2: Electric circuit can be defined as an interconnection between components or electrical devices for the purpose of communicating or transferring energy from one point to another. The components of electric circuit are always referred to as circuit elements.

International System of Units (SI) QuantityBasic UnitSymbol LengthMeterm MassKilogramkg TimeSeconds Electric currentAmpereA Thermodynamic temperature KelvinK Luminous intensityCandelacd

International System of Units (SI) MultiplierPrefixSymbol ExaE PetaP TeraT 10 9 GigaG 10 6 MegaM 10 3 Kilok 10 2 Hectorh 10 1 Dekada Decid Centid Milim Micro  Nanon Picop Femtof Attoa

Current and Voltage Figure 1.1: Two common types of signals (a)constant or direct current/voltage. (b)time-varying or alternating current/voltage.

Current and Voltage The electric current is the rate of change of charge over time, measured in amperes, A. Mathematically, current i, expressed in terms of charge, q and time, t is: i = dq/dt in coulomb/second or amperes.

Current and Voltage Voltage is defined as energy, w per unit charge, q created by the separation. Mathematically, we express this in differential form as: v = dw/dq in Joules/coulomb or volts

Power and Energy Reason why we should know about power and energy. 1st reason: Practically, any electrical devices have limitation in the power rating that they can handle. Exceeding the prescribed rating could destroy or make the device to malfunction. 2nd reason: We are paying our electrical bills to the power utility companies based on the amount of electric energy we consumed over a certain period of time. On top of all, we should realize that the useful output of our system is non-electrical form.

Power and Energy We define power as the time rate of expending (negative power) or absorbing (positive power) energy. P=dw/dt, in watts (W) The sign can be either positive or negative. +ve: The element is absorbing or dissipating (special case for a resistor) o or receiving power. -ve: The element is supplying or developing or expending or delivering or releasing power.

Ideal Basic Circuit Element Definition: Ideal – to imply that the element cannot exist as a realizable physical component. The purpose of its prescription is to model actual devices and systems. Basic – to imply that the circuit cannot be subdivided or further reduced into smaller parts.

Ideal Basic Circuit Element Types of Basic Circuit Element: Passive – elements are not capable of generating electrical energy. Resistor (dissipates energy) Capacitor and Inductor (can store or release energy) Active – elements capable of generating electrical energy. Voltage source Current source

Circuit Elements Active ElementsPassive Elements Independent sources Dependant sources A dependent source is an active element in which the source quantity is controlled by another voltage or current. They have four different types: VCVS, CCVS, VCCS, CCCS. Keep in minds the signs of dependent sources.

Ideal Basic Circuit Element Linear resistor: Resistor is passive element that dissipates electrical energy. Linear resistor is the resistor that obeys Ohm’s law. Capacitor: Capacitor is passive element designed to store energy in its electric field. It is normally used in tuning circuits of radio receivers and s dynamic memory elements in computer systems.

Ideal Basic Circuit Element Inductor: Inductor is another passive element designed to store energy in its magnetic field. Its numerous applications can be found in electronic and power systems such as power supplies, transformers, radars and electric motors.

Ideal Basic Circuit Element Voltage source Independent source This source maintains a specified voltage between its terminals but has no control on the current passing through it. The symbol of the independent voltage source is a plus-minus sign enclosed by a circle.

Ideal Basic Circuit Element Dependent voltage source This kind of voltage source has a specified voltage between its terminals but it is dependable on some other variable defined somewhere in the circuit. The symbol for the dependent voltage source is a plus-minus sign enclosed by a diamond shape. The value of the dependent current source is KVx (dimensionless) or Kix (ohms) where K is the scale factor or gain.

Ideal Basic Circuit Element Current source Independent current source This source maintains a specified current through its terminals but has no control on the voltage across its terminals. The symbol of the independent current source is an arrow enclosed by a circle.

Ideal Basic Circuit Element Dependent current source This kind of current source has a specified current between its terminals but it is dependent on some other variable defined somewhere in the circuit. The symbol for the dependent current source is an arrow enclosed by a diamond shape. The value of the dependent current source is KVx (in Siemens) or Kix (dimensionless) where K is the scale factor or gain.

Circuit Elements Example 1 Obtain the voltage v in the branch shown in Figure 1.1 for i 2 = 1A. Figure 1.1

Circuit Elements Solution Voltage v is the sum of the current-independent 10-V source and the current-dependent voltage source v x. Note that the factor 15 multiplying the control current carries the units Ω. Therefore, v = 10 + v x = (1) = 25 V

Ohm’s Law Ohm’s Law states that the voltage v across a resistor is directly proportional to the current I flowing through the resistor. V = I x R Where: V = VoltageVoltage I = CurrentCurrent R = ResistanceResistance

Kirchhoff’s Laws Kirchhoff’s Current Law Kirchhoff’s Current Law (KCL) states that the algebraic sum of current entering a node must be equal to that of leaving the same node. Applying KCL, we obtain; i2 + i6 = i1 + i3 + i4 + i5

Kirchhoff’s Laws Kirchhoff’s Voltage Law (KVL) Kirchhoff’s Voltage Law states that the algebraic sum of voltage drop in a loop must be equal to that of voltage rise in the same loop. Stated it in a different way is that the algebraic sum of all voltages around a loop must be zero. Applying KVL, we obtain; Loop 1: V1 + V2 + V3 = Vs Loop 2: V4 + VIs = V2