Power factor, cos Φ = \(\frac{R}{Z}\)

As Z increases, the power factor decreases.

Now, the average power over one cycle,

P_{av} = v_{rms} i_{rms} cos Φ

= V_{rms} \(\left(\frac{V_{\mathrm{rms}}}{Z}\right)\) cos Φ

= \(\frac{V_{\mathrm{rms}}^{2}}{\mathrm{Z}} \cos \phi\)

∴ P_{av} decreases as Z increases and cos Φ decreases.

As the current through the lamp \(\left(\frac{V_{\mathrm{rms}}}{Z}\right)\) decreases, the brightness of the lamp will decrease when C is increased