What is the voltage at the 90° point of a sine wave with a maximum voltage of 10V?

What is the voltage at the 90° point of a sine wave with a maximum voltage of 10V?

• A. -10V
• B. 0V
• C. 5V
• D. +10V

Answer: (D)

In a sine wave, the voltage can be represented mathematically by the formula \( V(t) = V_{max} \sin(\omega t + \phi) \), where \( V_{max} \) is the peak voltage, \( \omega \) is the angular frequency, \( t \) is time, and \( \phi \) is the phase angle. At the 90° point (or \(\frac{\pi}{2}\) radians) of the sine wave, the sine function reaches its maximum value. Given that the maximum voltage is 10V, at 90°, the sine function evaluates to 1. Therefore, the voltage at this point is calculated as: \[ V(90°) = 10V \cdot \sin(90°) = 10V \cdot 1 = 10V \] This indicates that at the 90° point, the sine wave reaches its peak of +10V. Understanding this concept is crucial in HVAC applications because knowing how voltage behaves in AC systems aids in diagnosing and troubleshooting electrical components.

In a sine wave, the voltage can be represented mathematically by the formula ( V(t) = V_{max} \sin(\omega t + \phi) ), where ( V_{max} ) is the peak voltage, ( \omega ) is the angular frequency, ( t ) is time, and ( \phi ) is the phase angle. At the 90° point (or (\frac{\pi}{2}) radians) of the sine wave, the sine function reaches its maximum value.

Given that the maximum voltage is 10V, at 90°, the sine function evaluates to 1. Therefore, the voltage at this point is calculated as:

[ V(90°) = 10V \cdot \sin(90°) = 10V \cdot 1 = 10V ]

This indicates that at the 90° point, the sine wave reaches its peak of +10V. Understanding this concept is crucial in HVAC applications because knowing how voltage behaves in AC systems aids in diagnosing and troubleshooting electrical components.