An AC voltage across a resistor in a radio circuit in volts is given by: V=4sin40πt
What is:
★ The peak voltage
★ The frequency
To determine the peak voltage, we need to find the maximum value of the sine function. In this case, the maximum value of sin40πt is 1, so the peak voltage is 4V.
To find the frequency, we need to look at the coefficient of t in the function. In this case, the coefficient is 40π. The frequency can be calculated by dividing this coefficient by 2π.
frequency = 40π / 2π = 20 Hz.
To find the peak voltage and frequency, let's analyze the equation V=4sin(40πt).
1. Peak Voltage:
The peak voltage represents the maximum value of the voltage. In the given equation, the coefficient of the sine term is 4. Therefore, the peak voltage is equal to the coefficient, so the peak voltage is 4 volts.
2. Frequency:
The frequency is a measure of how many cycles (or oscillations) occur per second. In the given equation, the frequency is determined by the coefficient inside the sine function.
The coefficient is 40π, which represents the angular frequency (ω) in radians per second. To find the frequency (f) in hertz (Hz), you need to divide the angular frequency by 2π.
So, the frequency (f) in hertz can be calculated as:
f = ω / (2π)
= 40π / (2π)
= 20 Hz.
Therefore, the frequency of the AC voltage is 20 Hz.