If a coil across a 500 cycle generator has an inductive reactance of 30 ohms, what will be the inductive reactance when the frequency is increased to 1000 cycles?

Inductive reactance is directly proportional to the frequency of the alternating current (AC) passing through an inductor. The formula for inductive reactance (XL) is given by:

[ XL = 2 \pi f L ]

where ( f ) is the frequency in hertz and ( L ) is the inductance in henries. When the frequency is increased, the inductive reactance also increases, and it does so in a linear fashion.

In this case, when the frequency changes from 500 cycles (Hz) to 1000 cycles (Hz), it doubles. Since the inductive reactance at 500 Hz is 30 ohms, at 1000 Hz, it will also double, leading to an inductive reactance of:

[ 30 , \text{ohms} \times 2 = 60 , \text{ohms} ]

Thus, the inductive reactance at a frequency of 1000 cycles is indeed 60 ohms. This reflects the fundamental relationship between frequency and inductive reactance, demonstrating that if the frequency is doubled, the inductive reactance also doubles. This relationship is essential in understanding how inductors behave in AC circuits under