Application of LCR Circuit: Here, we consider the Application of LCR Circuit containing a source, resistors, inductors and capacitors. Before discussing the formation of differential equation for the circuits, let us discuss the υ-i relationships for basic network elements. Resistor: The resistor shown in Fig. 11.1(a) has the following relation between voltage and current. where […]
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Non Homogeneous Differential Equation: Now let us consider the following Non Homogeneous Differential Equation, where the coefficients a0, a1, … an are constants, and f(t) is a function of me. The general solution may be written where xc is the complementary function, and xp is the particular integral. Since xc is the general solution of
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Homogeneous Linear Differential Equations: Consider an nth order homogeneous linear differential equations with constant coefficients, where a0, a1 … an are real constants. Now we shall find the solution of Eq. 11.11 of the form x = emt. By assuming that x = emt is a solution for certain m, we have Substituting in Eq. 11.11,
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Differential Equations Solutions and Basic Concepts: Differential Equations Solutions and Basic Concepts which denote rates of change, occur in various branches of science and engineering. We make use of differential equations, for example, to determine the motion of a rocket or a satellite, to determine the charge or current in an electric circuit, or to
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Parallel Magnetic Circuit: We have seen that a series magnetic circuit carries the same flux and the total mmf required to produce a given quantity of flux is the sum of the mmf’ s for the separate parts. In a Parallel Magnetic Circuit, different parts of the circuit are in parallel. For such circuits the
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Magnetic Leakage and Fringing: Magnetic Leakage and Fringing – Figure 10.28 shows a magnetized iron ring with a narrow air gap, and the flux which crosses the gap can be regarded as useful flux. Some of the total flux produced by the ring does not cross the air gap, but instead takes a shorter route
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Difference Between Electric Circuit and Magnetic Circuit: A Difference Between Electric Circuit and Magnetic Circuit are shown in Figs. 10.27(a) and (b) respectively. Figure 10.27(a) represents an electric circuit with three resistances connected in series, the dc source E drives the current I through all the three resistances whose voltage drops are V1,V2 and V3. Hence,
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Series Magnetic Circuit: A series magnetic circuit is analogous to a series electric circuit. Kirchhoff s laws are applicable to magnetic circuits also. Consider a ring specimen having a magnetic path of l meters, area of cross-section (A)m2 with a mean radius of R meters having a coil of N turns carrying I amperes wound
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Magnetic Circuit Analysis: Magnetic Circuit Analysis – The presence of charges in space or in a medium creates an electric field, similarly the flow of current in a conductor sets up a magnetic field. Electric field is represented by electric flux lines, magnetic flux lines are used to describe the magnetic field. The path of
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Doubled Tuned Coupled Circuits: Figure 10.24 shows a Doubled Tuned Coupled Circuits involving two series resonant circuits. For the circuit shown in the figure, a special case where the primary and secondary resonate at the same frequency ωr, is considered here, i.e. The two mesh equations for the circuit are From which or where A
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