Question

An electric lamp connected in series with a capacitor and an AC source glows with a certain brightness. (a) How does the average power change on increasing the capacitance? (b) How does the brightness of the lamp change on increasing the capacitance?

Answer 1

Impedance, Z = `sqrt(R^2 + 1/(ω^2C^2))`, where R is the resistance of the lamp, ω is the angular frequency of AC and C is the capacitance of the capacitor connected in series with the AC source and the lamp. When C is increased, `1/(ω^2C^2)` decreases. Hence, Z decreases.

Power factor, cos Φ = `R/Z`

As Z decreases, the power factor increases.

Now, the average power over one cycle,

`P_(av) = V_(rms)  i_(rms) cos Φ = V_(rms) ((V_(rms))/Z)`

cos Φ = `(V_(rms)^2)/Z` cos Φ

∴ P_av increases as Z decreases and cos Φ increases.  As the current through the lamp `(V_(rms)/Z)` increases, the brightness of the lamp will increase when C is increased.