A 50 V, 10 W lamp is run on 100 V, 50 Hz a.c. mains Calculate the inductance of the chock coil required.

Explanation

Voltage marked on lamp, V = 50 V
Power, P = 10 W
`therefore` Resistance of lamp, `R = (V^(2))/(P) = (50 xx 50)/(10) = 250 Omega`.
Current rating of lamp, `I_(rms) = (P)/(V) = (10)/(50) = (1)/(5)A`
The given circuit is equivalent to LR circuit.
Here `E_(rms) = 100 V, v = 50 Hz`
When the lamp is worked on a.c. the impedance of the circuit is
`Z_(L) = (E_(rms))/(I_(rms)) = (100)/((1)/(5)) = 500` ohm
`Z_(L)^(2) = R^(2) + omega^(2)L^(2)` ,
`Z_(L)^(2) = R^(2) + 4pi^(2)v^(2)L^(2)`
`rArr 4pi^(2) xx (50)^(2) L^(2) = 500^(2) - 250^(2) = 3 xx 250^(2)`
`rArr = (250sqrt(3))/(2pi xx 50) = (5sqrt(3))/(2pi) = 1.38 H`