EE101 - Electrical Sciences S. Sivasubramani Assistant Professor Electrical Engineering Department Indian Institute of Technology Patna Introduction In EE101, you will learn I Circuit analysis techniques with DC as well as Sinusoidal input. I Transient analysis of First order and second order circuits I Diode and its applications I Bipolar Junction Transistor (BJT) and how it is used as an amplifier I Operational amplifier(Op-amp) and its applications I Digital circuit design I Magnetic circuits, Transformers and its equivalent circuit model. This course is very important for EE students. For non EE students, the techniques and models used here will help you solve problems in your domain. Basic Definitions I Electric circuit : It is an interconnection of electrical components. I Electric current : It is time rate of change of charge. dq i = dt It is measured in Ampere (A). 1 A = 1 coulomb/second I i t t (a) Direct current (b) Alternating current Figure: Types of Current I Voltage (Potential difference): It is the energy required to move a unit charge through an element. dw v = dq It is measured in volts (V). 1 volt = 1 joule/ coulomb Like electric current, there are DC voltage and AC voltage. I Power: It is the time rate of expending or absorbing energy. dw dw dq p = = = v i dt dq dt It is measured in watts (W). 1 watts = 1 joule/second The power is the product of voltage across an element and the current through the element. I If the product is positive, the element is absorbing power. I If the product is negative, the element is delivering power. By passive sign convention 1. If the current enters the positive terminal of voltage polarity, p is positive and the element is absorbing power. 2. If the current leaves the positive terminal of voltage polarity, p is negative and the element is delivering power. i i + + v v − − (a) p = vi > 0 (b) p = vi < 0 Figure: Passive sign convention Circuit Elements There are two types of elements. 1. Active elements : They are capable of generating energy. Example : Generators and Batteries. 2. Passive elements : They are not capable of generating energy. Instead they can either absorb or store energy. Example: Resistors, Inductors, Capacitors. Active elements are modeled as either voltage source or current source. The voltage and current sources are further classified into independent and dependent sources. Ideal Independent Voltage Source It is an active element that maintains its terminal voltage constant irrespective of current it supplies. Example : Batteries and Generators i + V − V V v (a) (b) Figure: Symbols Figure: i-v characteristics Test yourself Draw the i − v characteristics. i i + R v V v + 1 V − Slope = R − V − R Ideal Independent Current Source It is an active element that supplies a certain current irrespective of its terminal voltage. Example : Solar cells i I I v Figure: Symbol Figure: i-v characteristics Test yourself Draw the i − v characteristics. i i + I × R I R v v 1 − Slope = R −I Ideal Dependent Voltage Source An ideal dependent or controlled voltage source is an active element. However its terminal voltage is controlled by another voltage or current + v − Figure: Symbol There are two types 1. Voltage Controlled Voltage Source 2. Current Controlled Voltage Source 1. Voltage Controlled Voltage Source (VCVS) A C + + vi vo − − B D vo = kvi 2. Current Controlled Voltage Source (CCVS) A C + ii vo − B D vo = rmii Ideal Dependent Current Source An ideal dependent or controlled current source is an active element. However its current is controlled by another voltage or current i Figure: Symbol There are two types 1. Voltage Controlled Current Source 2. Current Controlled Current Source 1. Voltage Controlled Current Source (VCCS) A + C vi io − D B io = gmvi 2. Current Controlled Current Source (CCCS) A C ii io D B io = kii Resistor R i + v − By Ohm's Law, v = iR Where R is the resistance in Ω. i 1 Slope = R v Figure: i − v characteristics When R = 0, + i v = iR v = 0 R = 0 v = 0 - It acts as a short circuit. When R = 1, i = 0 + v = iR v R = 1 i = 0 - It acts as an open circuit. Inductor L i + v − The voltage across an inductor using passive sign convention is di v = L dt where L is the inductance in henry (H). The important properties of an inductor 1. An inductor acts like a short circuit to DC. 2. The current through an inductor can not change instantaneously. Test yourself Draw the voltage across an inductor if the current through the inductor is i t v t Capacitor C i + − v The voltage across a capacitor using passive sign convention is dv i = C dt where C is the capacitance in farad (F). The important properties of a capacitor 1. A capacitor acts like an open circuit to DC. 2. The voltage across a capacitor can not change instantaneously. Test yourself Draw the current through a capacitor if the voltage across the capacitor is v t i t Branch It is an element. It can be either voltage source or current source or resistor. Node It is a point at which two or more branches are connected. Loop It is a closed path in a circuit. A loop is said to be independent if it does not contain any other loop inside. The number of independent loops (l) in a network can be found as given below. l = b − n + 1 where b and n are branches and nodes of the network respectively. Kirchhoff's Laws Kirchhoff's Current Law (KCL) The algebraic sum of currents entering a node or a closed boundary is zero. i4 i1 − i2 + i3 − i4 = 0 i1 i2 i1 + i3 = i2 + i4 i3 KCL is based on conservation of charge. KCL is true only when 1. there is no net charge accumulation at a node 2. the charge moves instantaneously Kirchhoff's Voltage Law (KVL) The algebraic sum of voltages around a cosed path or loop is zero. + v1 − −VA + v1 + VB + v2 = 0 VA VB v VA = v1 + VB + v2 − 2 + KVL is based on conservation of energy. KVL is true only when 1. there is no flux cutting the loop i.e., a conservative field. Elements in Series By Ohm's law, R1 R2 V1 = IR1; V2 = IR2 I + − + − By KVL, V1 V2 + V = V1 + V2 V − V = I (R1 + R2) = IReq where Req = R1 + R2. If N resistors are connected in series, Req = R1 + R2 + ··· + RN V I = R1 + R2 R1 R2 V1 = V ; V2 = V R1 + R2 R1 + R2 Elements in Parallel By Ohm's law, I V = I1R1 = I2R2 I1 I2 V V + I1 = ; I2 = V − R1 R2 R1 R2 By KCL, I = I1 + I2 R V V V I = 2 I I = + = 1 R + R R1 R2 Req 1 2 R1R2 R1 where Req = . I2 = I R1 + R2 R1 + R2 If N resistors are connected in parallel, 1 1 1 1 = + + ··· + Req R1 R2 RN.