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Electricity and Magnetism

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Charge flow in a Continuously Varying Current

EANDM-ADXBYJ

The current in a circuit has the following behavior as a function of time:

$$ I(t) = I_0 e^{- \alpha t}$$

What is the expression that gives the total charge,$Q_T$, that flows past a point in the circuit over the time interval from $t=0 \: \text s$ to $t=T$?

A

$Q_T =\cfrac { { I }_{ 0 } }{ \alpha } \left[ { e }^{ -\alpha T } -1\right] $

B

$Q_T ={ I }_{ 0 } \left[ 1-{ e }^{ -\alpha T } \right] $

C

$Q_T = { I }_{ 0 } \alpha \left[ { e }^{ -\alpha T } \right] $

D

$Q_T =\cfrac { { I }_{ 0 } }{ \alpha^2 } \left[ 1-{ e }^{ -2\alpha T } \right] $

E

$Q_T = \cfrac { { I }_{ 0 } }{ \alpha } \left[ 1-{ e }^{ -\alpha T } \right] $