If the current flowing through an element is given by: I(t) =3t A, 0≤t<6seconds
I(t) =18A, 6≤t<10seconds
I(t) =-12A, 10≤t<15seconds
I(t) =0,t≥15seconds
Plot the charge stored in the element over 0<t<20seconds.
To plot the charge stored in the element over 0 < t < 20 seconds, we need to first find the expression for the charge stored in the element at any given time.
The charge stored in an element can be found by integrating the current with respect to time. Since the current changes over different intervals, we'll need to split the time interval and calculate the charge for each interval separately.
Let's break down the time interval 0 < t < 20 seconds into the different intervals based on the given current function:
- For the interval 0 ≤ t < 6 seconds:
The current function is I(t) = 3t A.
The charge stored (Q) can be calculated by integrating I(t) with respect to t:
Q1 = ∫(3t) dt
= (3/2) * t^2
- For the interval 6 ≤ t < 10 seconds:
The current function is I(t) = 18 A.
The charge stored (Q) can be calculated by integrating I(t) with respect to t:
Q2 = ∫(18) dt
= 18t
- For the interval 10 ≤ t < 15 seconds:
The current function is I(t) = -12 A.
The charge stored (Q) can be calculated by integrating I(t) with respect to t:
Q3 = ∫(-12) dt
= -12t
- For the interval t ≥ 15 seconds:
The current function is I(t) = 0 A, indicating no charge is being stored.
Now, let's plot the charge stored over the 0 < t < 20 seconds interval:
Step 1: Create a time axis from 0 to 20 seconds.
Step 2: Calculate the charge stored for each interval and plot the corresponding value on the graph:
- For 0 ≤ t < 6 seconds:
Q1 = (3/2) * t^2
- For 6 ≤ t < 10 seconds:
Q2 = 18t
- For 10 ≤ t < 15 seconds:
Q3 = -12t
- For t ≥ 15 seconds:
Q = 0
Step 3: Connect the plotted points to visualize the variation in charge stored over time.
The resulting graph will show how the charge stored in the element changes over the given time intervals.
To plot the charge stored in the element over 0 < t < 20 seconds, we need to integrate the current function with respect to time.
First, let's define the function for the current as a piecewise function:
For 0 ≤ t < 6 seconds: I(t) = 3t A
For 6 ≤ t < 10 seconds: I(t) = 18 A
For 10 ≤ t < 15 seconds: I(t) = -12 A
For t ≥ 15 seconds: I(t) = 0
To find the charge, we need to integrate the current function with respect to time:
For 0 ≤ t < 6 seconds: Q(t) = ∫(0 to t) 3t dt = (1/2)t^2
For 6 ≤ t < 10 seconds: Q(t) = ∫(6 to t) 18 dt = 18(t - 6)
For 10 ≤ t < 15 seconds: Q(t) = ∫(10 to t) -12 dt = -12(t - 10)
For t ≥ 15 seconds: Q(t) = 0
Combining all the expressions for the charge, we can plot the charge stored in the element over 0 < t < 20 seconds. Here is the step-by-step process to plot the graph:
Step 1: Choose a time interval to plot the graph, here 0 < t < 20 seconds.
Step 2: Divide the interval into smaller sub-intervals based on the piecewise current function.
Step 3: For each sub-interval, calculate the charge using the respective expression.
Step 4: Plot the charge values on the y-axis against the corresponding time values on the x-axis.
Step 5: Connect the plotted points with a smooth curve.
Following the above steps, we can now plot the charge stored in the element over 0 < t < 20 seconds.