Question

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

Solution

Correct option is

The current ratting of the 20 V-5 W lamp is

            

                

And the resistance of its filament is  

          

                

If the lamp is to run on 200 V-50 Hz a.c. mains, a capacitor (or choke) must be placed in series in order to increase its effective (impedance) so that the current through it does not exceed 0.25 A. Let C be the capacitance of the required capacitor. Then, the impedance of the lamp-capacitor combination is  

              

                  

                 

                 

               

Now,  

           

  

               

   

   

.

SIMILAR QUESTIONS

Q1

An alternating voltage E = 200 sin 300t is applied across a series combination of  and L = 800 mH. Calculate the impedance of the circuit.

Q2

A coil of inductance 0.50 H and resistance  is connected to a 240 V-50 Hz a.c. supply. What are the maximum current in the coil and the time lag between voltage maximum and current maximum?

Q3

An emf E = 100 sin 314t volt is applied across a pure capacitor of 637 . Find the instantaneous current i.

Q4

An a.c. voltage V = 200 sin 314t is applied across a series C-R circuit.Where . Find the capacitive reactance.

Q5

In a series R-C circuit,  V = 100 V and . Find the current in the circuit and the voltage across the capacitor and the resistor. Is the algebraic sum of these voltages more than the source voltage? If yes, resolve the paradox. 

Q6

Calculate the rms current in an a.c. circuit containing a capacitor of  in series. The power supply in the circuit is rated 230 V, 50 Hz.

Q7

An alternating rms current of 1.5 mA and angular frequency  flows through a  capacitor in series. Calculate the rms voltage across the capacitor and the impedance of the circuit.

Q8

When an alternating voltage of 220 V is applied across a device X, a current 0.5 A flows through the circuit and is in phase with the applied voltage. When the same voltage is applied across another device Y, again the same current flows but it leads the voltage by . Compute the current in the circuit when the same voltage in applied across the series combination of X and Y.

Q9

 capacitor in series with a  resistor is connected to a 110V-60 Hz supply. What is the maximum current in the circuit? What is the time lag between current maximum and voltage maximum?   

Q10

An alternating emf of frequency 50 Hz is applied to a series circuit ofresistance , an inductance of 100 mH and a capacitance of . Does the current lag or lead the emf and by what angle?