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Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 Chapter Contents Introduction Currents whose direction does not change with time through a load, are known as direct current (D.C.), whereas currents whose direction changes periodically through a load are known as alternating currents and the voltage is known as alternating voltage (ac voltage). Most of the electrical devices require ac voltage because electrical energy in a.c. form can be easily transmitted over long distances without much loss. A.C. voltage can be easily converted to other voltages by step up/step down transformers. ALTERNATING CURRENT Alternating Current : An alternating current is one which changes in magnitude continuously with time and reverses its direction periodically and is abbreviated as a.c. The source of alternating emf may be a dynamo or an electronic oscillator. The alternating emf E at any instant may be expressed as E = E0 sin t where  is angular frequency of alternating emf and E0 is the peak value or amplitude of alternating emf. The frequency of alternating emf, f = /2 and time period of alternating emf., 1 2 T f     . Introduction Alternating Current A.C. Voltage Applied to a Resistor AC Voltage Applied to an Inductor AC Voltage Applied to a Capacitor AC Voltage Applied to a Series LCR Circuit Power in AC Circuits : The Power Factor LC Oscillations Parallel LC Circuit (Rejector Circuit) Transformers Chapter 22 Alternating Current
128 Alternating Current NEET Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 The alternating current in a circuit, fed by an alternating source of emf may be controlled by inductance L, resistance R and capacitance C. Due to presence of elements L and C, the current is not necessarily in phase with the applied emf. Therefore alternating current is, in general expressed as I = I 0 sin (t + ) where  is the phase which may be positive, zero or negative depending on the value of reactive components L, R and C. Calculation of mean and rms values for some specific cases of a.c. 1. For a current varying as shown in the graph, the mathematical expression may be given as t T i i        2 0 Now let us calculate mean value for positive half cycle 0 mean 0 t t i dt i dt    t I T 3 2T 2 T T 2 i0 –i 0         2/ 0 0 mean 2 2 T tdt T i T i  2 0 mean i i  To calculate rms value 1 2 2 0 rms 0                  t t i dt i dt         2/ 0 2 2 0 rms 2 2 T t dt T i T i  3 0 rms i i  2. For sinusoidal a.c. I mean = 0 for one complete cycle t T/2 T I0 I Sine curve O I mean =  2 0I for half cycle I rms = 2 0I 3. For the out put of a half wave rectifier I mean =  0I for one complete cycle I mean =  2 0I for t = 0 to t = T/2 t /2 TT I Sine curve O I rms = 2 0I for one complete cycle
NEET Alternating Current 129 Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 4. For the out-put of a full wave rectifier I mean =  2 0I t T/2 T I Sine curve I0 O I rms = 2 0I for one complete cycle 5. For the square wave shown in figure I mean = 0 for one complete cycle I mean = I 0 for t = 0 to t = T/2 t /2 TT I I0 Square wave –I0 O I rms = I 0 for one complete cycle I rms = I 0 for t = T/2 to t = T Note : Whenever you are asked to calculate charge flown in a circuit then mean value of alternating current comes into picture. Phasor Any quantity that varies sinusoidally, can be represented as the projection of a uniform circular motion on a diameter of the circular path. To represent an alternating emf, the peak value E0 is taken as radius vector of the circle. When this radius vector E0 rotates with angular velocity  as shown in figure, the projection on the diameter along y-axis gives instantaneous value of emf. y-axis E t 0sin t x-axis '' E0 A.C. VOLTAGE APPLIED TO A RESISTOR Let a.c. voltage applied is v = vm sint ... (i) ~ I R where vm is the maximum value of applied voltage (or amplitude of oscillating potential difference) and  is the angular frequency.  vm I R        sin t = i m sint ... (ii)
130 Alternating Current NEET Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 Im I v 2  t vm where m m v I R        is the amplitude of current. From Eq. (i) & (ii), it is clear that voltage across the resistor and current through the resistor are in same phase. The sum of the instantaneous current values over one complete cycle is ZERO and thus the average of the current over one complete cycle is ZERO. The instantaneous power dissipated in the resistor is p = I 2R = I m 2Rsin2t ... (iii) The average value of ‘p’ over a cycle is 2 2 2 m rms I pI R R   ... (iv) Example 1 : A light bulb has the rating 200 W, 220 V. Find (i) resistance of the bulb filament (ii) rms value of current flowing through the filament. Solution : (i) 2 V R P  220 220 200   22 22 2     242 (ii) The rms value of current = P V 200 220  10 A =0.9 A 11  EXERCISE 1. The voltages of domestic ac is 220 V. What does this represent? (1) Mean voltage (2) Peak voltage (3) Root mean voltage (4) Root mean square voltage 2. The equation of an alternating voltage is V = 100 2 sin 100t volt. The RMS value of voltage and frequency will be respectively (1) 100 V, 50 Hz (2) 50 V, 100 Hz (3) 150 V, 50 Hz (4) 200 V, 50 Hz