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| Summary |
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 An alternating current is that which changes continuously in magnitude and periodically in direction. It can be represented by a sine curve or a cosine curve i.e., |
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| I = Iosinwt or I = Io = coswt |
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| Here, Io is peak value of current and I is instantaneous value of current. |
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| w = 2p/T = 2pv |
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| where T is period of a.c and v is frequency of a.c. The alternating EMF can similarly be represented as |
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| E = Eo sinwt or Eo coswt |
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 The root mean square (r.m.s) value of alternating current is defined as that value of steady current, which would generate the same amount of heat in a given resistance in a given time, as is done by the alternating current, when passed through the same resistance for the same time. The r.m.s value of a.c. is also called effective value or virtual value of a.c. It is represented by Irms, Ieff or Iv. It can be shown that |
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| Similarly, |
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| All a.c. instruments measure virtual values of a.c. The behavior of an ohmic resistance R in a.c. circuit is the same as in d.c. circuit. Through alternating EMF and alternating current are in same phase. |
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 Inductive reactance (XL) is the resistance offered by an inductor and is given by |
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| XL = wL = 2pvL |
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| Through a pure inductor, alternating current lags behind the alternating EMF by phase angle of 90o. |
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 Capacitative reactance (Xc) is the resistance offered by a capacitor and is given by |
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| Through a pure capacitor, alternating current leads the alternating EMF by a phase angle of 90o. XL and Xc both are measured in ohms. |
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 The total effective resistance of RLC circuit is called Impedance (Z) of the circuit. It is given by |
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| The angle by which alternating voltage leads the alternating current in RLC circuit is given by |
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 Impedance triangle is a right-angled triangle whose base represents ohmic resistance R, perpendicular represents reactance (XL-Xc) and hypotenuse represents impedance (z) of the RLC circuit. From this triangle, we can calculate z and f as stated above. |
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 When a condenser of capacity C charged to a certain potential is connected to an inductor L, energy stored in C oscillates between L and C. The frequency of energy oscillations is given by |
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| If there is no loss of energy, total energy in L and C at every instant remains constant. |
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 A circuit in which inductance L, capacitance C and resistance R are connected in series and the circuit admits maximum current, is called series resonant circuit. The necessary condition for resonance is |
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| XL = Xc. |
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| which gives |
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| i.e., frequency of a.c. fed to the circuit becomes equal to natural frequency of energy oscillations in the circuit. |
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| Under this condition, |
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| The series resonance circuit is used as an acceptor circuit in ratio and T.V receiver sets. |
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| The sharpness of turning at resonance is measured by Q factor or quality factor of the circuit. It is given by |
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 Average power associated over a complete cycle in a non inductive circuit (containing R, L, C with XL = XC) or pure resistive circuit is |
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| P = Ev Lv |
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| On the contrary, average power associated over a complete cycle with a pure inductor or pure capacitor is zero. Hence current through L and through C is said to be wattless or Idle current. |
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| In an inductor, energy stored during growth of current is |
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| This is spent in maintaining the current during decay. |
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| In a capacitor, energy stored during charging is |
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| This is spent during discharging of the condenser. In an LCR circuit, average power associated over a complete cycle is |
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| P = Eu Iv cosQ |
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| where Q is phase angle between alternating voltage and alternating current in the circuit, cosQ = p / Ev Iv = true power / apparent power, is called power factor of the a.c. circuit. The value of power factor varies from 0 to 1. |
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 An a.c. generator / dynamo produces alternating current energy from mechanical energy of rotation of a coil. It is based on the phenomenon of EMI. The form of EMF induced is |
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| e = e sinwt, |
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| where e = NABw max EMF induced. Here, N is total number of turns in the coil, A is area of the coil, B is strength of magnetic field applied and w is angular velocity of the armature coil. |
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 A choke coil is a pure inductor used for controlling current in an a.c. circuit. Through pure L, phase difference between E and I is Q = 90o |
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| Average power consumed/cycle |
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| For reducing low frequency alternating current, choke coils with laminated soft iron cores are used, and for reducing high frequency alternating currents, air cored chokes are used. |
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 A transformer is an electrical device, which is used for changing alternating voltages. |
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| It is based on the phenomenon of mutual induction. If ns is number of turns in secondary, then |
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| For a step up transformer k>1 and for a step down transformer, k<1. The main use of transformer is in transmission of a.c. over long distances, at extremely high voltages. This reduces the energy losses in transmission. |
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