When we talk about the "Rate of Change," we refer to how a quantity changes with respect to time or another variable. It's like measuring speed - you want to know how fast or slow something is happening. For the alternating voltage problem, this means figuring out how quickly the voltage, given by the equation \( v = 100 \sin(200t) \), changes over time.
To do this, we calculate something called the derivative, which tells us the rate at which one quantity changes with respect to another. Here, it helps us find how fast the voltage changes as time goes by.
- The rate at \( t = 0.005 \text{s} \) was around 10806 volts per second, telling us the voltage was increasing at that moment.
- At \( t = 0.01 \text{s} \), the rate was around -8322 volts per second, indicating the voltage was decreasing then.
These numbers provide us an insight into the behavior of the voltage over time, showing whether it's ramping up or down at any given point.