An electric bulb rated 100 W, 40 V has to be operated across 50 V, 50 Hz A.C. supply. What is the value of inductance of inductor connected in series with the bulb?
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Given:
An electric bulb rated 100 W, 40 V has to be operated across 50 V, 50 Hz A.C. supply.
To find:
What is the value of inductance of inductor connected in series with the bulb?
Solution:
From given, we have,
An electric bulb rated 100 W, 40 V
P = 100 W, V = 40V
P = VI
100 = 40 × I
I = 100/40 = 2.5 A
It has to be operated across 50 V, 50 Hz A.C. supply.
V = 50 V, f = 50 Hz
Z = V/I = 50/2.5 = 20 Ω
R = V/I = 40/2.5 = 16 Ω
X{L} = √[Z² - R²] = √[20² - 16²] = 12 Ω
wL = X{L}
L = X{L}/2πf
L = 12/(2 × 3.14 × 50}
L = 0.03 H
Therefore, the value of inductance of inductor connected in series with the bulb is 0.03 H
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