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Valhalla
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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?
[tex]t_0=0[/tex]
[tex]i_0=5A[/tex]
[tex]t_f=14400s[/tex]
[tex]i_f=1A[/tex]
[tex]\frac{i_f-i_0}{t_f-t_0} =\frac{-4A}{14400}[/tex]
[tex]q=\int_{0}^{14400}(\frac{-1A}{3600}t+5)dt[/tex]
[tex]q= \left[\frac{-1}{7200}t^2+5t\right]_{0}^{14400}[/tex]
[tex]q= 43200C[/tex]
That seems like a whole lot of charge. I know it is a long period of time. Can anyone see anything wrong with this?
[tex]t_0=0[/tex]
[tex]i_0=5A[/tex]
[tex]t_f=14400s[/tex]
[tex]i_f=1A[/tex]
[tex]\frac{i_f-i_0}{t_f-t_0} =\frac{-4A}{14400}[/tex]
[tex]q=\int_{0}^{14400}(\frac{-1A}{3600}t+5)dt[/tex]
[tex]q= \left[\frac{-1}{7200}t^2+5t\right]_{0}^{14400}[/tex]
[tex]q= 43200C[/tex]
That seems like a whole lot of charge. I know it is a long period of time. Can anyone see anything wrong with this?
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