A `20` volts `5` watt lamp(lamp to be treated as a resistor) is used on `AC` mains of `200` volts and `50/pisqrt11 c.p.s` Calculate the (i)capacitance of the capacitor, or inductance of the inductance, to be put in series to run the lamp.(ii)How much pure resistance should be included in place of the above device so that the lamp can run on its rated voltage.(iii)which is more economical (the capacitor the inductor or the resistor).

Answer

(i)`125/33 muF` or `2.4 H` , (ii)`720 Omega` , (iii)it will be more economical to use inductance or capacitance in series with the lamp to run it as it.It consumes no power while there would be dissipation of power when resistances is inserted in series with the lamp.

Explanation

(i)`[1/(omegaC)xxI_(rms)]^(2)+[20]^(2)=[200]^(2)` where `I_(rms)=5/20` & `omega=2pixx50/pisqrt11`
or `[(omegaL)I_(rms)]^(2)+(20)^(2)=200^(2)`
(iii)`I_(rms)xxR+20=200`
(iii)does not loos in `C` in `L`.