Question

Find the value of t at which the stored energy has 1/e of the value you found in part g

Answer 1

The value of
`\( t \)` at which the stored energy has
`\( (1)/(e) \)` of the value found in part g is given by
`\( t = -(1)/(\lambda) \ln\left((1)/(e)\right) \).`

Step-by-step explanation:

In the given question, the stored energy as a function of time
`\( t \)` is likely expressed using an exponential function involving
`\( \lambda \)`. To find the time at which the stored energy has
`\( (1)/(e) \)` of its maximum value, we set the expression for stored energy equal to
`\( (1)/(e) \)` times the maximum value and solve for
`\( t \).`

The formula
`\( t = -(1)/(\lambda) \ln\left((1)/(e)\right) \)` is derived from the fact that the natural logarithm of
`\( (1)/(e) \)` is equal to -1. This time value corresponds to the point in time when the stored energy has decayed to
`\( (1)/(e) \)` of its maximum value. The negative sign indicates a decay or decrease in energy over time.

It's crucial to understand the mathematical relationship between the exponential function, natural logarithm, and the concept of
`\( (1)/(e) \)` to interpret and apply the formula correctly in the context of the stored energy function.