Question

A choke coil is needed to operate an arc lamp at $160V$ (rms) and $50Hz$. The arc lamp has an effective resistance of $5\Omega$ when running at $10A$ (rms). Calculate the inductance of the choke coil. If the same arc lamp is to be operated on $160V$ DC, what additional resistance would be required. Compare the power losses in both the cases.

Answer 1

We know that
$I_{rms}=\frac{V_{rms}}{\sqrt{R^2+{\omega }^2{L}^2}}$
$\therefore 10=\frac{160}{\sqrt{25+{(2\pi \times 50\times L)}^2}}or25+{\left(100\pi L\right)}^2={16}^2$
$\Rightarrow 25+{10}^5{L}^2=256\Rightarrow L=\sqrt{\frac{231}{{10}^5}}=0.05H$
Let $R_A$ be the additioal resistance required for operating the arc lamp with $160V$ DC source, then
$10=\sqrt{\frac{160}{R_A+5}}\Rightarrow R_A+5=16\therefore R_A=16-5=11\Omega$
AC power consumed by the arc lamp $=V_{rms}{I}_{rms}\cos \varphi =P_{ac}$
where $\cos \varphi =\frac{R}{Z}=\frac{R}{\sqrt{R^2+{\omega }^2{L}^2}}=\frac{5}{16}$
$P_{ac}=160\times 10\times \frac{5}{16}=500W$
Now DC power consumed by arc lamp
$P_{dc}=160\times 10=1600W$
Power loss $=1600=500=110W=68.75$%