Simple current and charge circuit question

AI Thread Summary
The discussion revolves around calculating the total charge that passes a point in a wire over a specified time interval, given the current function i(t) = 4t + 5. Initially, the user calculated the current at specific times but did not account for the integration needed to find total charge. The correct approach involves integrating the current function over the interval from t=0 to t=10 seconds, which results in a total charge of 250C, as indicated in the textbook. The user expresses confusion about the need for integration but ultimately realizes the mistake after revisiting the physics concepts. Understanding the relationship between current, charge, and time through integration is crucial for accurate calculations in electrical circuits.
JFonseka
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Homework Statement


If the current in a wire is given by the following functions of time, what charge passes
a given point from t=0 to t=10 seconds? (i is in Amps and t in seconds). Show units
for charge.

i(t) = 4t + 5


Homework Equations



Nothing really

The Attempt at a Solution



0 seconds: 5A
10 seconds: 4x10 + 5 = 45A

Therefore 50C have passed through the wire in total.
But the answer at the back for my question says 250C, I don't get it.
 
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You have to integrate that formula with respect to time, then plug in a value for t.
 
Ah...now I see that I get the right answer...but why do we have to integrate. I don't get it.
 
Nvm I just realized. This is what happens when you stay out of touch with physics for 4 months.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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