An alternating voltage is given by: v=100 sin200 t volts,...

An alternating voltage is given by: $v=100 \sin 200 t$ volts, where $t$ is the time in seconds. Calculate the rate of change of voltage when (a) $t=0.005 \mathrm{~s}$ and (b) $t=0.01 \mathrm{~s}$

Key Concepts

Sinusoidal Waveform

A sinusoidal waveform is a smooth periodic oscillation that is commonly used to represent alternating voltages and currents. In electrical engineering, such representations like v = 100 sin(200t) model how voltage varies cyclically with time. This concept is central in understanding the behavior of AC power systems as well as in signal processing.

Differentiation of Functions

Differentiation is a fundamental concept in calculus that involves finding the rate at which a function changes with respect to a variable. When a function represents a physical quantity, such as voltage, its derivative signifies the rate of change of that quantity, which is essential for analyzing dynamics in various systems.

Chain Rule

The chain rule is a method used in calculus to differentiate composite functions. When a function is composed of an outer function and an inner function—such as the sine function with a time-dependent argument—the chain rule is applied to correctly compute the derivative. This rule is critical when finding the rate of change of sinusoidal functions in time.

Angular Frequency

Angular frequency is a parameter that describes how quickly the phase of a waveform changes with time, usually measured in radians per second. In the expression for an alternating voltage, the angular frequency appears as the coefficient of time in the sine or cosine functions, indicating how fast the waveform oscillates, which in turn affects the derivative of the voltage.

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