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Consider the circuit containing a pure inductive coil of inductance L Henry. When an alternating voltage V (RMS) is applied across the coil, an alternating current I (RMS) will flow through the circuit. Due to this alternating current, a back emf (e) is induced in the coil due to inductance of it. This back emf at every instant opposes the any change in current through the coil.Let the applied alternating voltage is$$\mathrm{u=V_{m}sin\:\omega t}\:\:\:… (1)$$The back emf (e) induced in the inductor coil is given by, $$\mathrm{e=L \frac{di}{dt}}\:\:\:… (2)$$Since, there is no ohmic drop, thus the applied voltage has to overcome ... Read More
In order to differentiate the diamagnetism, paramagnetism, and ferromagnetism, first we need to understand, the concept of magnetism and diamagnetism, paramagnetism and ferromagnetism individually.Concept of MagnetismElectrons exhibit two types of angular momenta − Orbital Angular Momenta and Spin Angular Momenta . The orbital angular momentum is a property of electrons when they are in atoms while the spin angular momentum is an intrinsic property of electrons. With these angular momenta, a magnetic moment is associated. That magnetic moment is a property which causes the electrons to experience a force, when they are placed in a magnetic field.The orbital magnetic moment ... Read More
Electric NetworkAn electrical network is an interconnection of electrical components (like sources, resistors, inductors, capacitors, diodes, transistors etc.). An electrical network need not contain a closed path for the flow of electric current. Some examples of the network are shown in the figure given below.Characteristics of Electric NetworkAn electric network possesses the following characteristics −It is an interconnection of electrical components.Electric network need not provide a return path for the current.It may or may not contain active electrical components.It may be consist of, passive elements, active elements or both active and passive elements.Examples of electric network are − Resistive network, ... Read More
ProblemDraw the state transition diagram over an alphabet Σ={a, b} that accepts the string starting with ‘ab’.SolutionThe formal definition of Deterministic Finite Automata (DFA) is as follows −A DFA is a collection of 5-tuples as shown below −M=(Q, Σ, δ, q0, F)Where, Q: Finite set called states.Σ: Finite set called alphabets.δ: Q × Σ → Q is the transition function.q0 ∈ Q is the initial state.The language is generated as given below −L={ab, aba, abab, …….}The transition diagram is as follows −Here, D is a dead state.D is a transition state, which it can never escape. Such a state is ... Read More
Non-deterministic finite automata also have five states which are same as DFA, but with different transition function, as shown follows −δ: Q X Σ -> 2QNon-deterministic finite automata is defined as a 5 tuple, M=(Q, Σ, δ, q0, F)Where, Q: Finite set of statesΣ: Finite set of the input symbolq0: Initial stateF: Final stateδ: Transition function: Q X Σ -> 2QProblemDesign a transition diagram and table for the given language that accepts all strings of length at least 2.SolutionBefore proceeding to the solution, let’s understand what do you mean by length of string and how to find the length of ... Read More
A Deterministic Finite automata (DFA) is a collection of defined as a 5-tuples and is as follows −M=(Q, Σ, δ, q0, F)Where, Q: Finite set called states.Σ: Finite set called alphabets.δ: Q × Σ → Q is the transition function.q0 ∈ Q is the start or initial state.F: Final or accept state.Example 1The DFA accepts all strings starting with 0The language L= {0, 01, 001, 010, 0010, 000101, …}In this language, all strings start with zero.Transition diagramThe transition diagram is as follows −ExplanationStep 1 − q0 is the initial state on input ‘0’ it goes to q1, which is the ... Read More
A string is a finite set sequence of symbols choosen from some alphabets.For example, 00011001 is a string from binary alphabet Σ={0, 1}aabbcabcd is a string from alphabet Σ={a, b, c, d}The different operations performed on strings are explained below −Concatenation.Substring.Kleen star operation.Reversal.ConcatenationConcatenation is nothing but combining the two strings one after another.ExampleLet’s consider two strings −X= TutorialsY= PointThe concatenation (X, Y) of two strings is −X.Y = TutorialsPointNote − Concatenation of empty string with other string gives string itself.For example, X. ε = ε.X = XSubstringIf ‘w’ is a string then ‘v’ is substring of ‘w’ if there exists ... Read More
A finite state machine has a set of states and two functions called the next-state and output function.The set of states correspond to all the possible combinations of the internal storage. If there are n bits of storage, there are 2n possible states.The next state function is a combinational logic function that, given the inputs and the current state, determines the next state of the system.The diagram given below explains the functioning of a finite state machine in TOC.The output function generates a set of outputs from the current state and the inputs.TypesThe two types of finite state machines are ... Read More
There are two methods for converting a Deterministic Finite Automata (DFA) to Regular expression (RE). These methods are as follows −Arden's Theorem Method.State Elimination Method.Let us understand the Arden's Theorem method in detail.Arden's TheoremLet P and Q be the two regular expressions.If P does not contain null string, then the following equation in R, viz R = Q + RP, Which has a unique solution by R = QP*Here, The finite automata (FA) does not have epsilon moves.It must have only initial state q1.Its states are q1, q2, q3, ....qn. The final state may be some qi where i QP* ... Read More
If Σ is an alphabet, the set of all strings can be expressed as a certain length from that alphabet by using exponential notation. The power of an alphabet is denoted by Σk and is the set of strings of length k.For example, Σ ={0, 1}Σ1= {0, 1} ( 21=2)Σ2= {00, 01, 10, 11} (22=4)Σ3= {000, 001, 010, 011, 100, 101, 110, 111} (23= 8)The set of strings over an alphabet Σ is usually denoted by Σ*(Kleene closure)For instance, Σ*= {0, 1}*={ ε, 0, 1, 00, 01, 10, 11, ………}Therefore, Σ*= Σ0U Σ1U Σ2U Σ3…………. With ε symbolThe set of ... Read More