Assignment on AC

Alternating current

Assignment

Q 1. In a series LCR circuit the emf is leading the current for a particular frequency of operation.  

        You now lower the frequency slightly. Does the total impedance of the circuit increase,    

         decrease, or stay the same? Give reason.                                                                                (1)

Q2. Why would power distribution systems be less effective without alternating current?  (1)

Q 3. Discuss in your own words what it means to say that an a.c. leads or lags an alternating     

         emf.                                                                                                                                                 (1)

Q 4. State which of the two, the capacitor or an inductor, tends to become SHORT when the   

         frequency of the applied alternating voltage has a high value? And why?                             (1)

Q 5. Why power correction is must in heavy machinery ?                                                              (1)

Q 6. Prove that average value of ac over a complete cycle is zero.                                               (2)

Q 7. An inductor L of reactance X_L , is connected in series with a bulb B to an ac source. Briefly    

        explain how does the brightness of the bulb change when (i) number of turns of the    

        inductor is reduced and (ii) a capacitor of same reactance is included in series in the same  

        circuit.          (2)

Q 8. A transformer of 100% efficiency has 200 turns in the primary and 4000 turns in the

        secondary. It is connected to a 220V main supply and the secondary feeds to a 100 kilo-   

        ohm resistance. Calculate the output potential difference per turn and power delivered to

        the load.               (3)

Q 9. A 20V-5W lamp is to run on 200V-50Hz ac mains. Find the capacitance of a capacitor   

        required to run the lamp.                                                                                                             (3)

Q10. (a) A series LCR circuit is connected to an ac source of variable frequency. Draw a suitable  

               phasor diagram to deduce the expressions for the amplitude of the current and phase  

               angle.

         (b) obtain the condition of resonance. draw a plot showing the variation of current with

               the frequency of ac source for two resistances R1 and R2 (R1>R2). Hence define the  

               quality factor and write its role in tuning of the circuit.                                               (5)

Q11. (a) Show that energy is conserved in LC oscillations.

          (b) when a circuit element ‘ X ’ is connected across an a.c. source, a current of A flows   

                through it and this current is in phase with the applied voltage. When another element

                ‘Y’ is connected across the same a.c. source, the same current flows in the circuit but it  

                leads the voltage by π/2 radians.

                      (i) Name the circuit elements X and Y.

                      (ii) Find the current that flows in circuit when the series combination of X and Y is  

                             connected across the same a.c. source.

                      (iii) plot a graph showing the variation of net impedance of this series combination   

                            of X and Y as a function of the angular frequency of the applied voltage.        (5)