An arc lamp requires a direct current of $10\, A$ at $80 \,V$ to function. If it is connected to a $220 \,V \,(rms)$, $50 \,Hz\, AC$ supply, the series inductor needed for it to work is close to :
- 80 H
- 0.08 H
- 0.044 H
- 0.065 H
The Correct Option is D
Solution and Explanation
$R = \frac{80}{10} = 8 \omega$
For $ac$
$10 = \frac{220}{\sqrt{R^{2} + \omega^{2}L^{2}}} $
$R^{2} + \omega^{2}L^{2} = \left(\frac{220}{10}\right)^{2}$
$ L^{2} = \frac{22^{2} - 8^{2}}{\omega^{2}} $
$\therefore L = \frac{\sqrt{30 \times14}}{2 \pi\times50} = \frac{\sqrt{420}}{100 \pi} = 0.065\, H $
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Concepts Used:
Alternating Current
An alternating current can be defined as a current that changes its magnitude and polarity at regular intervals of time. It can also be defined as an electrical current that repeatedly changes or reverses its direction opposite to that of Direct Current or DC which always flows in a single direction as shown below.
Alternating Current Production
Alternating current can be produced or generated by using devices that are known as alternators. However, alternating current can also be produced by different methods where many circuits are used. One of the most common or simple ways of generating AC is by using a basic single coil AC generator which consists of two-pole magnets and a single loop of wire having a rectangular shape.
Application of Alternating Current
AC is the form of current that are mostly used in different appliances. Some of the examples of alternating current include audio signal, radio signal, etc. An alternating current has a wide advantage over DC as AC is able to transmit power over large distances without great loss of energy.