Question

The voltage E in an electrical circuit is modeled by E = 1.5×cos 140×pi×t, where t is time measured in seconds. Find the frequency. (The number of cycles (periods) completed in 1 sec is the frequency of the function.)

a) 70 Hz
b) 140 Hz
c) 35 Hz
d) 280 Hz

Answer 1

The frequency of the electrical circuit described by E = 1.5×cos 140×pi×t is 70 Hz when the argument of the cosine function is compared to the formula for angular frequency.

Step-by-step explanation:

The frequency of an electrical circuit, where the voltage E is modeled by E = 1.5×cos 140×pi×t, is found by examining the argument of the cosine function. The general form of the voltage function here is E = A×cos(2π×f×t), where A is the amplitude, f is the frequency, and t is the time. The term 2π×f represents the angular frequency and is equivalent to the numeric value given in the equation, which is 140×pi. To find the frequency, we say 2π×f = 140×pi. Solving for f, we get f = (140×pi) / (2π) = 70 Hz. Therefore, the correct answer is (a) 70 Hz.