What is the frequency of electric current of alternating current I = 200 sin(60πt + π/6)? FM communication frequency band range for FM broadcast is? What will the focal length of a... What is the frequency of electric current of alternating current I = 200 sin(60πt + π/6)? FM communication frequency band range for FM broadcast is? What will the focal length of a convex lens whose power is +2.5D? What is the path difference equivalent to 4π phase difference?
Understand the Problem
The question is asking about the frequency of electric current given in a specific mathematical form, as well as other physics concepts related to FM broadcast frequency and focal length of a lens. It requires identifying the correct answer based on provided options.
Answer
The frequency
Answer for screen readers
The frequency of the electric current is ( 30 , \text{Hz} ).
Steps to Solve
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Identify the wave function The given current function is ( I = 200 \sin(60\pi t + \frac{\pi}{6}) ).
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Understand the angular frequency The general form of the sine function for alternating current is ( I = A \sin(\omega t + \phi) ), where ( \omega = 60\pi ) radians per second is the angular frequency.
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Calculate the frequency To find the frequency ( f ), use the relationship between angular frequency and frequency: $$ \omega = 2\pi f $$ So, $$ 60\pi = 2\pi f $$
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Solve for frequency Divide both sides by ( 2\pi ): $$ f = \frac{60\pi}{2\pi} = 30 \text{ Hz} $$
The frequency of the electric current is ( 30 , \text{Hz} ).
More Information
In alternating current, the frequency indicates how many cycles occur in one second. The function describes the oscillation of current, with the angular frequency revealing the speed of the cycles.
Tips
- Confusing angular frequency with frequency: Remember, ( \omega = 2\pi f ) relates the two.
- Not converting from radians to Hz properly. Ensure you use the correct formulas.
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