Calculating Total Charge Flowing Through Circuit

[Valhalla]

In this problem assume that current is linearly proportional to time. The intial condition at time 0 is 5A. At time 4 hours the current is 1A. What is the total charge that flows through this circuit?

$$t_0=0$$
$$i_0=5A$$
$$t_f=14400s$$
$$i_f=1A$$

$$\frac{i_f-i_0}{t_f-t_0} =\frac{-4A}{14400}$$

$$q=\int_{0}^{14400}(\frac{-1A}{3600}t+5)dt$$

$$q= \left[\frac{-1}{7200}t^2+5t\right]_{0}^{14400}$$

$$q= 43200C$$

That seems like a whole lot of charge. I know it is a long period of time. Can anyone see anything wrong with this?

 

[quasar987]

1A is a very large current too. It looks fine to me.

 

[kyle8921]

I can confirm that the calculations and assumptions made in this problem are correct. The total charge flow through the circuit can be calculated by integrating the current function over the given time period. The resulting value of 43200C seems reasonable, considering the initial and final current values and the length of time. However, it is always important to double check calculations and assumptions to ensure accuracy. Additionally, it would be helpful to provide units for the time and current values to avoid confusion.