LR circuit

Brightness decreases when an iron rod is inserted in the coil, as the inductance and hence the impedance of the circuit increases.
It increases when the frequency of the AC source is decreased, as the impedance decreases.
It increases when the number of turns in the coil is reduced, as the impedance decreases.
It increases when a capacitance of reactance $X_C = X_L$ is included, as the impedance decreases.

Inductive reactance $X_L = 2\pi fL$ is proportional to frequency.
At 50 Hz, $X_L = 20\ \Omega$; at 100 Hz, $X_L' = 20\times\frac{100}{50} = 40\ \Omega$
The resistance does not depend on frequency: R = 30 $\Omega$.
Impedance at 100 Hz: $Z = \sqrt{R^2 + X_L'^2} = \sqrt{30^2 + 40^2} = \sqrt{2500} = 50\ \Omega$
$I = \frac{V}{Z} = \frac{200}{50}$
I = 4.0 A

In a series LR circuit the voltage leads the current by an angle $\phi$ given by $\tan\phi = \frac{X_L}{R}$
$\tan\phi = \frac{3}{3} = 1$
$\phi = 45^\circ$
$\phi = \frac{\pi}{4}$