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A bulb connected to 50 V d.c. consumes 2...

A bulb connected to 50 V d.c. consumes 20 W power. Then the bulb is connected to a capacitor in an a.c. power supply of 250 V, 50 Hz. Find the value of the capacitor required so that the bulb drows the same amount of current.
Data : P = 20 W, V = 50 V, v = 50 Hz, C = ?

Text Solution

Verified by Experts

`P = VI`
`:. I = (P)/(V) = (20)/(50) = 0.4A`
`:.` Resistance, `R = (V)/(I) = (50)/(0.4) = 125 Omega`

The impedance, `Z = (V)/(I) = (250)/(0.4) = 625 Omega`
`:. Z = sqrt(R^(2) + ((1)/(omega C))^(2)) = sqrt(R^(2) + ((1)/(2pi v C))^(2))`
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