Answer
49,300 C or 49.3 kC
Work Step by Step
Charge (Coulomb) = Current (ampere) x Time (seconds)
Since the current is non-constant, we need to find the area of each section to determine the total charge of the graph.
For Area 1 (trapezoid), the following dimensions are true:
base 1 (a) = 6 amperes
base 2 (b) = 10 amperes
height (h) = 0.5 hour x 3,600 seconds per hour = 1,800 seconds
Solving the area, the formula is below:
Area = $\frac{a+b}{2}$ $\times$ h
Area = $\frac{6+10}{2}$ $\times$ 1,800
Area = 14,400 C or 14.4 kC
For Area 2 (trapezoid), the following dimensions are true:
base 1 (a) = 4 amperes
base 2 (b) = 6 amperes
height (h) = 1.5 hour x 3,600 seconds per hour = 5,400 seconds
Note: height h is the difference between 2 hours and 0.5 hours
Solving the area, the formula is below:
Area = $\frac{a+b}{2}$ $\times$ h
Area = $\frac{4+6}{2}$ $\times$ 5,400
Area = 27,700 C or 27.7 kC
For Area 3 (right triangle), the following dimensions are true:
base (b) = 4 amperes
height (h) = 1 hour x 3,600 seconds per hour = 3,600 seconds
Note: height h is the difference between 2 hours and 1 hour
Solving the area, the formula is below:
Area = $\frac{1}{2}$ $\times$ b $\times$ h
Area = $\frac{1}{2}$ $\times$ 4 $\times$ 3,600
Area = 7,200 C or 7.2 kC
Total Area = Total Charge = Area 1 + Area 2 + Area 3
Total Charge = 14.4 kC + 27.7 kC + 7.2 kC
Total Charge = 49.3 kC
