Question

Military aircraft use\({\rm{400}}\;{\rm{Hz}}\)AC power because it is possible to design lighter-weight equipment at this higher frequency. What is the time for one complete cycle of this power?

Short answer

The time period of the AC power of the military aircraft is \({\rm{T = 2}}{\rm{.50\;ms}}\).

Step-by-step solution

Given Data

The frequency of the AC power is \(400\;{\rm{Hz}}\)

Relation between time period and frequency.

The period T of an AC waveform is the amount of time it takes to complete one cycle. It is related to the frequency f of the wave as follows:

\({\bf{T = }}\frac{{\bf{1}}}{{\bf{f}}}\)

Calculation for the time period for the military aircraft.

The time for one complete cycle of the power is found from the equation:

\(T = \frac{1}{f}\)

For the given value of\(f\)

\(\begin{array}{c}T = \frac{1}{{400\;{\rm{Hz}}}}\\ = 2.50 \times {10^{ - 3}}\;{\rm{s}}\\ = \left( {2.50 \times {{10}^{ - 3}}\;{\rm{s}}} \right)\left( {\frac{{{{10}^3}\;{\rm{ms}}}}{{1\;{\rm{s}}}}} \right)\\ = 2.50\;{\rm{ms}}\end{array}\)

Therefore,the time period of the military aircraft is\({\rm{2}}{\rm{.50\;ms}}\).