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

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

• A. -10V
• B. 0V
• C. +10V
• D. 5V

Answer: (C)

A sine wave has a distinct shape characterized by its maximum and minimum values, and it oscillates between these extremes. The maximum voltage, also known as the peak voltage, in this case is given as 10V. At a 90-degree point on the sine wave, which corresponds to the first quarter of the cycle, the sine function reaches its peak value. The sine function can be represented mathematically as: \[ V(t) = V_{max} \cdot \sin(θ) \] Where \( V_{max} \) is the maximum voltage and \( θ \) is the angle in degrees. At 90 degrees, the sine of that angle is equal to 1: \[ V(90°) = 10V \cdot \sin(90°) = 10V \cdot 1 = 10V \] This confirms that at 90 degrees, the voltage is at its maximum of +10V. Understanding the characteristics of a sine wave, including its maximum, zero-crossing, and minimum points, is crucial when analyzing AC voltages, particularly in HVACR applications where such waveforms are common.

A sine wave has a distinct shape characterized by its maximum and minimum values, and it oscillates between these extremes. The maximum voltage, also known as the peak voltage, in this case is given as 10V.

At a 90-degree point on the sine wave, which corresponds to the first quarter of the cycle, the sine function reaches its peak value. The sine function can be represented mathematically as:

[ V(t) = V_{max} \cdot \sin(θ) ]

Where ( V_{max} ) is the maximum voltage and ( θ ) is the angle in degrees. At 90 degrees, the sine of that angle is equal to 1:

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

This confirms that at 90 degrees, the voltage is at its maximum of +10V. Understanding the characteristics of a sine wave, including its maximum, zero-crossing, and minimum points, is crucial when analyzing AC voltages, particularly in HVACR applications where such waveforms are common.