Introduction of a series capacitor in the lamp circuit with inductance will reduce the overall impedance presented to the power supply and if such an act is not part of the original design, it would likely increase the current through the lamp above its design value with consequent reduction in its rated life due to nature of tungsten filaments at the lamp ends.

slope does increase with frequency

assume 2 signals, unit magnitude 1A

f1 = 1 Hz

f2 = 10 Hz

start at zero crossing

1/4 cycle positive slope, then 1/2 cycle negative, the 1/4 positive, repeat

let's focus on the first 1/4 positive

time duration for 1 cycle: 1/1 = 1 sec, 1/4 cycle = 0.25 or 1/4

f1 di/dt ~ delta I / delta t = 1/(1/4) = 4 A/sec

time duration for 1 cycle: 1/10 = 0.1 sec, 1/4 cycle = 0.025 or 1/40

f2 di/dt ~ delta I / delta t = 1/(1/40) = 40 A/sec

much 'steeper'

another way to look at this

Xl = j (2 Pi f) L

as f increases, so does X and it 'chokes' or suppresses the higher frequencies

it can be said as 'slope' (di/dt) increases so does impedance