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UNIT-4, LOCUS DIAGRAMS, RESONANCE AND MAGNETIC CIRCUITS, •, •, •, •, •, •, , Locus Diagrams with variation of various parameters, Series RC and RL circuits, Parallel RLC circuits, Resonance, Series and Parallel circuits, Concept of Bandwidth and Quality factor, , CBIT, , EEE, , PDTR

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Locus Diagrams with variation of various parameters:, Introduction: In AC electrical circuits the magnitude and phase of the current vector depends upon, the values of R,L&C when the applied voltage and frequency are kept constant. The path traced by the, terminus (tip) of the current vector when the parameters R,L&C are varied is called the current, Locus diagram . Locus diagrams are useful in studying and understanding the behavior of the RLC, circuits when one of these parameters is varied keeping voltage and frequency constant., In this unit, Locus diagrams are developed and explained for series RC,RL circuits and Parallel LC circuits, along with their internal resistances when the parameters R,L and C are varied., The term circle diagram identifies locus plots that are either circular or semicircular. The defining, equations of such circle diagrams are also derived in this unit for series RC and RL diagrams., In both series RC,RL circuits and parallel LC circuits resistances are taken to be in series with L and C to, highlight the fact that all practical L and C components will have at least a small value of internal, resistance., Series RL circuit with varying Resistance R:, Refer to the series RL circuit shown in the figure (a) below with constant XL and varying R. The current IL, lags behind the applied voltage V by a phase angle Ɵ = tan-1(XL/R) for a given value of R as shown in the, figure (b) below. When R=0 we can see that the current is maximum equal to V/XL and lies along the I, axis with phase angle equal to 900. When R is increased from zero to infinity the current gradually, reduces from V/XL to 0 and phase angle also reduces from 900 to, 00. As can be seen from the figure, the tip of the current vector traces the path of a semicircle, with its diameter along the +ve I axis., , Fig 4.1(a): Series RL circuit with, variation of R, Varying Resistance R, , CBIT, , Fig 4.1(b): Locus of current vector IL with, , EEE, , PDTR

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The related equations are:, IL = V/Z, Sin Ɵ = XL/Z or Z = XL/ Sin Ɵ and Cos Ɵ = R / Z, Therefore IL = (V/XL) Sin Ɵ, For constant V and XL the above expression for ILis the polar equation of a circle with diameter (V/XL) as, shown in the figure above., Circle equation for the RL circuit: (with fixed reactance and variable Resistance):, The X and Y coordinates of the current IL are IX =, IL Sin Ɵ, IY = IL Cos Ɵ, From the relations given above and earlier we get, IX = (V/Z )( X L/Z) = V XL/Z2 ---------------------------- (1), and, IY = (V/Z )( R/Z), = V R/Z2--------------------------- (2), Squaring and adding the above two equations we get, I 2 + I 2 = V2(X 2+R2) / Z4 = (V2Z2 )/ Z4 = V2/Z2 -------------------------- (3), X, , Y, , L, , From equation (1) above we have Z2 = V XL / IX and substituting this in the above equation (3) we get :, IX2 + IY2 = V2/ (V XL / IX ) = (V/XL) IX, or, IX2+ IY2 −(V/XL) IX, =0, Adding (V/2XL)2 to both sides ,the above equation can be written as, [IX −V/2XL ]2+ IY2 = (V/2XL)2 ---------------------------------- (4), Equation (4) above represents a circle with a radius of (V/2XL) and with it’s coordinates of the, centre as (V/2XL , 0), Series RC circuit with varying Resistance R:, Refer to the series RC circuit shown in the figure (a) below with constant XC and varying R. The current IC, leads the applied voltage V by a phase angle Ɵ = tan-1(XC/R) for a given value of R as shown in the figure, (b) below. When R=0 we can see that the current is maximum equal to −, V/XC and lies along the negative I axis with phase angle equal to −900. When R is increased, from zero to infinity the current gradually reduces from −V/XC to 0 and phase angle also reduces, from −900 to 00. As can be seen from the figure, the tip of the current vector traces the path of a, semicircle but now with its diameter along the negative I axis., Circle equation for the RC circuit: (with fixed reactance and variable Resistance):, Inthesame way as wegotfortheSeries RLcircuit with varying resistancewe canget thecircle equation, for an RC circuit with varying resistance as :, [IX + V/2XC ]2+ IY2 = (V/2XC)2, whose coordinates of the centre are (−V/2XC , 0) and radius equal to V/2XC, , CBIT, , EEE, , PDTR

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Fig 4.2 (a): Series RC circuit with, Varying Resistance R, , Fig 4.2 (b): Locus of current vector IC, with variation of R, , Series RL circuit with varying Reactance X L:, Refer to the series RL circuit shown in the figure (a) below with constant R and varying XL. The current IL, lags behind the applied voltage V by a phase angle Ɵ = tan-1(XL/R) for a given value of R as shown in the, figure (b) below. When XL =0 we can see that the current is maximum equal to V/R and lies along the, +ve V axis with phase angle equal to 00. When XL is increased from zero to infinity the current, gradually reduces from V/R to 0 and phase angle increases from 00 to 900. As can be seen from the, figure, the tip of the current vector traces the path of a semicircle with its diameter along the +ve, V axis and on to its right side., , Fig 4.3(a): Series RL circuit with varying X L Fig 4.3(b) : Locus of current vector I L with, variation of XL, , CBIT, , EEE, , PDTR

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Series RC circuit with varying Reactance X C:, Refer to the series RC circuit shown in the figure (a) below with constant R and varying XC. The current IC, leads the applied voltage V by a phase angle Ɵ= tan-1(XC/R) for a given value of R as shown in the figure, (b) below. When XC =0 we can see that the current is maximum equal to V/R and lies along the V axis, with phase angle equal to 00. When XC is increased from zero to, infinity the current gradually reduces from V/R to 0 and phase angle increases from 00 to −900., As can be seen from the figure, the tip of the current vector traces the path of a semicircle with, its diameter along the +ve V axis but now on to its left side., , Fig 4.4(a): Series RC circuit with varying XC, variation of XC, , Fig 4.4(b): Locus of current vector IC with, , Parallel LC circuits:, Parallel LC circuit along with its internal resistances as shown in the figures below is considered here for, drawing the locus diagrams. As can be seen, there are two branch currents IC and IL along with the, total current I. Locus diagrams of the current IL or IC (depending on which arm is varied)and the total, current I are drawn by varying RL, RC , XL and XC one by one., Varying XL:, , Fig 4.5(a): parallel LC circuit with Internal Resistances RL and RC in series with L (Variable) and, C (fixed) respectively., CBIT, , EEE, , PDTR

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The current IC through the capacitor is constant since RC and C are fixed and it leads the voltage vector OV, by an angle ƟC = tan-1 (XC/RC) as shown in the figure (b). The current IL through the inductance is the, vector OIL .It’s amplitude is maximum and equal toV/RLwhen XL is zeroand it is in phase with the applied, voltage V. When XLis increased from zero to infinity it’s amplitude decreases to zero and phase will be, lagging the voltage by 900. In between, the phase angle will be lagging the voltage V by an angle ƟL=, tan-1(XL/RL). The locus of the current vector IL is a semicircle with a diameter of length equal to V/RL., Note that this is the same locus what we got earlier for the series RL circuit with XL varying except that, here V is shown horizontally., Now, to get the locus of the total current vector OI we have to add vectorially the currents IC and IL ., We know that to get the sum of two vectors geometrically we have to place one of the vectors staring, point (we will take varying amplitude vector IL)at the tip of the other vector (we will take constant, amplitude vector IC)and then join the start of fixed vector IC to the end of varying vector IL. Using, this principle we can get the locus of the total current vector OI by shifting the IL semicircle starting, point O to the end of current vector OIC keeping the two diameters parallel. The resulting semi, circle ICIBT shownin thefigureindottedlines isthelocus of the total current vector OI., , Fig 4.5(b): Locus of current vector I in Parallel LC circuit when XL is varied from 0 to ∞, , Varying XC:, CBIT, , EEE, , PDTR

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Fig.4.6(a) parallel LC circuit with Internal Resistances RL and RC in series with L (fixed) and C, (Variable) respectively., , The current IL through the inductor is constant since RL and L are fixed and it lags the voltage vector OV, by an angle ƟL = tan-1(XL/RL) as shown in the figure (b). The current IC through the capacitance is the, vector OIC . It’s amplitude is maximum and equal to V/RC when XC is zero and it is in phase with the applied, voltage V. When XCis increased from zero to infinity it’s amplitude decreases to zero and phase will be, leading the voltage by 900. In between, the phase angle will be leading the voltage V by an angle ƟC=, tan-1(XC/RC). The locus of the current vector IC is a semicircle with a diameter of length equal to V/RC as, shown in the figure below. Note that this is the same locus what we got earlier for the series RC circuit, with XCvarying except that here V is shown horizontally., Now, to get the locus of the total current vector OI we have to add vectorially the currents IC and IL ., We know that to get the sum of two vectors geometrically we have to place one of the vectors staring, point (we will take varying amplitude vector IC)at the tip of the other vector (we will take constant, amplitude vector IL) and then join the start of the fixed vector IL to the end of varying vector IC. Using, this principle we can get the locus of the total current vector OI by shifting the IC semicircle starting, point O to the end of current vector OIL keeping the two diameters parallel.The resulting semicircle, ILIBT shown in the figure in dotted lines is the locus of the total current vector OI., , CBIT, , EEE, , PDTR

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Fig4.6 (b) : Locus of current vector I in Parallel LC circuit when X C is varied from 0 to ∞, Varying RL :, The current IC through the capacitor is constant since RC and C are fixed and it leads the voltage vector OV, by an angle ƟC = tan-1 (XC/RC) as shown in the figure (b). The current IL through the inductance is the, vector OIL . It’s amplitude is maximum and equal to V/XL when RL is zero. Its phase will be lagging the, voltage by 900. When RL is increased from zero to infinity it’s amplitude decreases to zero and it is in, phase with the applied voltage V. In between, the phase angle will be lagging thevoltage V by an angle ƟL, = tan-1(XL/RL). The locus of the current vector IL is a semicircle with a diameter of length equal to V/RL., Note that this is the same locus what we got earlier for the series RL circuit with R varying except that, here V is shown horizontally., , CBIT, , EEE, , PDTR

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Fig. 4.7(a) parallel LC circuit with Internal Resistances RL (Variable) and RC (fixed) in series, with L and C respectively., Now, to get the locus of the total current vector OI we have to add vectorially the currents IC and IL ., We know that to get the sum of two vectors geometrically we have to place one of the vectors staring, point (we will take varying amplitude vector IL)at the tip of the other vector (we will take constant, amplitude vector IC)and then join the start of fixed vector IC to the end of varying vector IL. Using, this principle we can get the locus of the total current vector OI by shifting the IL semicircle starting, point O to the end of current vector OIC keeping the two diameters parallel. The resulting, semicircle ICIBT shown in thefigure in dotted linesis thelocus of the total current vector OI., , Fig 4.7(b) : Locus of current vector I in Parallel LC circuit when R L is varied from 0 to ∞, Varying R C:, , CBIT, , EEE, , PDTR

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Fig. 4.8(a) parallel LC circuit with Internal Resistances RL (fixed) and RC (Variable), with L and C respectively., , in series, , The current IL through the inductor is constant since RL and L are fixed and it lags the voltage vector OV, by an angle ƟL = tan-1(XL/RL) as shown in the figure (b). The current IC through the capacitance is the, vector OIC . It’s amplitude is maximum and equal to V/XC when RC is zero and its phase will be leading the, voltage by 900 . When RC is increased from zero to infinity it’s amplitude decreases to zero and it will, be in phase with the applied voltage V. In between, the phase angle will be leading the voltage V by an, angle ƟC = tan-1 (XC/RC). The locus of the current vector IC is a semicircle with a diameter of length equal, to V/XC as shown in the figure below. Note that this is the same locus what we got earlier for the, series RC circuit with R varying except that here V is shown horizontally., Now, to get the locus of the total current vector OI we have to add vectorially the currents IC and IL ., We know that to get the sum of two vectors geometrically we have to place one of the vectors staring, point (we will take varying amplitude vector IC)at the tip of the other vector (we will take constant, amplitude vector IL) and then join the start of the fixed vector IL to the end of varying vector IC. Using, this principle we can get the locus of the total current vector OI by shifting the IC semicircle starting, point O to the end of current vector OIL keeping the two diameters parallel.The resulting semicircle, ILIBT shown in the figure in dotted lines is the locus of the total current vector OI., , CBIT, , EEE, , PDTR

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Fig 4.8(b) : Locus of current vector I in Parallel LC circuit when R C is varied from 0 to ∞, , Resonance:, Series RLC circuit:, Theimpedanceof theseriesRLC circuit showninthefigurebelowandthe currentIthroughthe circuit, are given by :, Z = R + jωL +1 /jωC = R + j ( ωL − 1/ωC), I = Vs/Z, , Fig 4.9: Series RLC circuit, The circuit is said to be in resonance when the Inductive reactance is equal to the Capacitive, reactance. i.e. XL = XC or ωL = 1/ωC. (i.e. Imaginary of the impedance is zero) The frequency at, which the resonance occurs is called resonant frequency. In the resonant condition when XL, = XC they cancel with each other since they are in phase opposition(1800 out of phase) and net, impedance of the circuit is purely resistive. In this condition the magnitudes of voltages across, CBIT, , EEE, , PDTR

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the Capacitance and the Inductance are also equal to each other but again since they are of opposite, polarity they cancel with each other and the entire applied voltage appears across the Resistance alone., Solving for the resonant frequency from the above condition of Resonance : ωL = 1/ωC, 2πfrL = 1/2πfrC, 2, 2, fr = 1/4π LC, and, fr = 1/2π√LC, In a series RLC circuit, resonance may be produced by varying L or C at a fixed frequency or by, varying frequency at fixed L and C., Reactance, Impedance and Resistance of a Series RLC circuit as a function of frequency:, From the expressions for the Inductive and capacitive reactance we can see that when the, frequency is zero, capacitance acts as an open circuit and Inductance as a short circuit. Similarly when the, frequency is infinity inductance acts as an open circuit and the capacitance acts as a short circuit. The, variation of Inductive and capacitive reactance along with Resistance R and the Total Impedance are, shown plotted in the figure below., As can be seen, when the frequency increases from zero to ∞ Inductive reactance XL (directly, proportional to ω) increases from zero to ∞ and capacitive reactance XC (inversely proportional to ω), decreases from −∞ to zero. Whereas, the Impedance decreases from ∞ to Pure, Resistance R as the frequency increases from zero to fr ( as capacitive reactance reduces from, −∞ and becomes equal to Inductive reactance ) and then increases from R to ∞ as the frequency, increases from fr to ∞ (as inductive reactance increases from its value at resonant frequency to ∞ ), , Fig 4.10: Reactance and Impedance plots of a Series RLC circuit, Phase angle of a Series RLC circuit as a function of frequency:, , CBIT, , EEE, , PDTR

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Fig4.11 : Phase plot of a Series RLC circuit, The following points can be seen from the Phase angle plot shown in the figure above:, •, •, , •, •, , At frequencies below the resonant frequency capacitive reactance is higher than the, inductive reactance and hence the phase angle of the current leads the voltage., As frequency increases from zero to fr the phase angle changes from -900 to zero., At frequencies above the resonant frequency inductive reactance is higher than the, capacitive reactance and hence the phase angle of the current lags the voltage., As frequency increases from fr and approaches ∞, the phase angle increases from zero and, approaches 900, , Band width of a Series RLC circuit:, The band width of a circuit is defined as the Range of frequencies between which the output power, is half of or 3 db less than the output power at the resonant frequency. These frequencies are, called the cutoff frequencies, 3db points or half power points. But when we consider the output, voltage or current, the range of frequencies between which the output voltage or current falls to, 0.707 times of the value at the resonant frequency is called the Bandwidth BW. This is because, voltage/current are related to power by a factor of √2 and, when we are consider √2 times less it becomes 0.707. But still these frequencies are called, as cutoff frequencies, 3db points or half power points. The lower end frequency is called lower, cutoff frequency and the higher end frequency is called upper cutoff frequency., , CBIT, , EEE, , PDTR

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i.e., , 2L (ω2 – ω1) = 2R, , i.e. (ω2 – ω1), , Or finally Band width, , = R/L, , and, , (f2 – f1) = R/2πL ----------(6), , BW = R/2πL ------------------------------------------- (7), , Since fr lies in the centre of the lower and upper cutoff frequencies f1 and f2 using the above equation, (6) we can get:, f1 = fr – R/4πL, , ------, , (8), , f2 = fr + R/4πL, , ------, , (9), , Further by dividing the equation (6) above by fr on both sides we get another important, relation :, (f2 – f1) / fr = R/2π fr L, or BW / fr = R/2π fr L ---------------- (10), Here an important property of a coil i.e. Q factor or figure of merit is defined as the ratio of the, reactance to the resistance of a coil., Q = 2π fr L / R -------------------------------(11), Now using the relation (11) we can rewrite the relation (10) as, Q = fr / BW --------------------------------- (12), , Quality factor of a series RLC circuit:, The quality factor of a series RLC circuit is defined as:, Q = Reactive power in Inductor (or Capacitor) at resonance / Average power at Resonance, , Reactive power in Inductor at resonance = I2XL, Reactive power in Capacitor at resonance = I2XC, Average power at Resonance, , = I2R, , Here the power is expressed in the form I2X (not as V2/X) since I is common through R.L and C in the, series RLC circuit and it gets cancelled during the simplification., Therefore Q = I2XL / I2R = I2XC / I2R, Q = XL / R = ωr L/ R ------------------------------------------- (1), Or Q = XC / R = 1/ωr RC ---------------------------------- (2), From these two relations we can also define Q factor as :, CBIT, , EEE, , PDTR

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Q = Inductive (or Capacitive ) reactance at resonance / Resistance, Substituting the value of ωr = 1/√LC in the expressions (1) or (2) for Q above we can get the value, of Q in terms of R, L,C as below., Q = (1/√LC ) L/ R, , = (1/R) (√L/C), , Selectivity:, Selectivity of a series RLC circuit indicates how well the given circuit responds to a given resonant, frequency and how well it rejects all other frequencies. i.e. the selectivity is directly proportional to, Q factor. A circuit with a good selectivity (or a high Q factor) will have maximum gain at the resonant, frequency and will have minimum gain at other frequencies .i.e. it will have very low band width. This, is illustrated in the figure below., , Fig 4.13: Effect of quality factor on bandwidth Voltage Magnification at resonance:, At resonance the voltages across the Inductance and capacitance are much larger than the applied, voltage in a series RLC circuit and this is called voltage magnification at Resonance. The voltage, magnification is equal to the Q factor of the circuit. This is proven below., If we take the voltage applied to the circuit as V and the current through the circuit at resonance, as I then, The voltage across the inductance L is:, VL = IXL = (V/R) ωr L and, The voltage across the capacitance C is:, VC = IXC = V/R ωr C, But we know that the Q of a series RLC circuit = ωr L/ R = 1/R ωr C Using, these relations in the expressions for VL and VC given above we get VL = VQ, and VC = VQ, The ratio of voltage across the Inductor or capacitor at resonance to the applied voltage in a series, RLC circuit is called Voltage magnification and is given by, Magnification = Q = VL/V or VC / V, CBIT, , EEE, , PDTR

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Important points In Series RLC circuit at resonant frequency :, •, •, •, •, , The impedance of the circuit becomes purely resistive and minimum i.e Z = R, The current in the circuit becomes maximum, The magnitudes of the capacitive Reactance and Inductive Reactance become equal, The voltage across the Capacitor becomes equal to the voltage across the Inductor at, resonance and is Q times higher than the voltage across the resistor, , Bandwidth and Q factor of a Parallel RLC circuit:, Parallel RLC circuit is shown in the figure below. For finding out the BW and Q factor of a parallel, RLC circuit, since it is easier we will work with Admittance , Conductance and Susceptance instead, of Impedance ,Resistance and Reactance like in series RLC circuit., , Fig 4.14 : Parallel RLC circuit, Then we have the relation:, , Y = 1/Z = 1/R + 1/jωL + jωC = 1/R + j ( ωC −1/ωL), , For the parallel RLC circuit also, at resonance, the imaginary part of the Admittance is zero and hence, the frequency at which resonance occurs is given by: ωrC −1/ωrL = 0 . From this we get : ωrC, = 1/ωrL and ωr = 1/√LC, which is the same value for ωr as what we got for the series RLC circuit., At resonance when the imaginary part of the admittance is zero the admittance becomes, minimum.( i.e Impedance becomes maximum as against Impedance becoming minimum in series, RLC circuit ) i.e. Current becomes minimum in the parallel RLC circuit at resonance ( as against current, becoming maximum in series RLC circuit) and increases on either side of the resonant frequency as, shown in the figure below., , CBIT, , EEE, , PDTR

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Fig 4.15: Variation of Impedance and Current with frequency in a Parallel RLC circuit, Here also the BW of the circuit is given by BW = f2-f1 where f2 and f1 are still called the upper and lower, cut off frequencies but they are 3db higher cutoff frequencies since we notice that at, these cutoff frequencies the amplitude of the current is √2 times higher than that of the, amplitude of current at the resonant frequency., The BW is computed here also on the same lines as we did for the series RLC circuit:, If the current at points P1 and P2 is √ 2 (3db) times higher than that of Imin( current at the resonant, frequency) then the admittance of the circuit at points P1 and P2 is also √2 times higher than the, admittance at fr ), But amplitude of admittance at point P1 is given by: Y = √1/R2 + (1/ω1L - ω1C )2 and equating this to √, 2 /R weget, 1/ω1L − ω1C, , = 1/R ---------------- (1), , Similarly amplitude of admittance at point P2 is given by: Y = √1/R2 + (ω2C −1/ω2L)2 and equating, this to √2 /R we get, ω2C −1/ω2L, , = 1/R ---------------- (2), , Equating LHS of (1) and (2) and further simplifying we get, 1/ω1L − ω1C, , = ω2C − 1/ω2L, , 1/ω1L + 1/ω2L, , = ω1C + ω2C, , 1/L [(ω1 + ω2)/ ω1ω2] = (ω1 + ω2)C, 1/L C = ω1ω2, , CBIT, , EEE, , PDTR

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Substituting the value of ωr = 1/√LC in the expressions (1) or (2) for Q above we can get the value, of Q in terms of R, L,C as below., Q = (1/√LC ) RC, , = R (√C/L), , Further using the relation Q = ωr RC ( equation 2 above ) in the earlier equation (1) we got in BW, viz. (f2-f1)/ fr = 1/2π fr RC we get :, (f2-f1)/ fr = 1/Q or Q = fr / (f2-f1) = fr / BW, i.e. In Parallel RLC circuit also the Q factor is inversely proportional to the BW., , Admittance, Conductance and Susceptance curves for a Parallel RLC circuit as a function of, frequency :, •, •, •, •, •, •, , The effect of varying the frequency on the Admittance, Conductance and Susceptance of a parallel, circuit is shown in the figure below., Inductive susceptance BL is given by BL = - 1/ωL. It is inversely proportional to the frequency ω, and is shown in the in the fourth quadrant since it is negative., Capacitive susceptance BC is given by BC = ωC. It is directly proportional to the frequency ω, and is shown in the in the first quadrant as OP .It is positive and linear., Net susceptance B = BC - BL and is represented by the curve JK. Ascan be seen it is zero atthe, resonant frequency fr, The conductance G = 1/R and is constant, The total admittance Y and the total current I are minimum at the resonant frequency as, shown by the curve VW, , CBIT, , EEE, , PDTR

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Fig 4.16: Conductance, Susceptance and Admittance plots of a, Parallel RLC circuit Current magnification in a Parallel RLC circuit:, Just as voltage magnification takes place across the capacitance and Inductance at the, resonant frequency in a series RLC circuit, current magnification takes place in the, currents through the capacitance and Inductance at the resonant frequency in a, Parallel RLC circuit. This is shown below., Voltage across the Resistance = V = IR, Current through the Inductance at resonance IL = V/ ωr L = IR / ωr L = I . R/ ωr, L = I Q Similarly, Current through the Capacitance at resonance IC = V/ (1/ωr C ) = IR / (1/ωr C ) = I(R ωr, C) = I Q, From which we notice that the quality factor Q = IL / I or IC / I and that the current, through the inductance and the capacitance increases by Q times that of the current, through the resistor at resonance. ., Important points In Parallel RLC circuit at resonant frequency :, •, •, •, •, , The impedance of the circuit becomes resistive and maximum i.e Z = R, The current in the circuit becomes minimum, The magnitudes of the capacitive Reactance and Inductive Reactance become equal, The current through the Capacitor becomes equal and opposite to the current, through the Inductor at resonance and is Q times higher than the current through, the resistor, Magnetic Circuits:, Introduction to the Magnetic Field:, Magnetic fields are the fundamental medium through which energy is converted from, one form to another in motors, generators and transformers. Four basic principles, describe how magnetic fields are used in these devices., , 0. A current-carrying conductor produces a magnetic field in the area around it., Explained in Detail by Fleming’s Right hand rule and Amperes Law., 1. A time varying magnetic flux induces a voltage in a coil of wire if it passes through, that coil. (basis of Transformer action), Explained in detail by the Faradays laws of Electromagnetic Induction., 2. A current carrying conductor in the presence of a magnetic field has a force induced in, CBIT, , EEE, , PDTR

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it ( Basis of Motor action), 3. A moving wire in the presence of a magnetic field has a voltage induced in it (, Basis of Generator action), , CBIT, , EEE, , PDTR