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anonymous

  • 5 years ago

The current through a 4F capacitor is given by the equation i(t)=5e^(-t/2) for t>0. Assuming that the capacitor is is initially uncharged, determine an expression for the voltage across the capacitor.

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  1. anonymous
    • 5 years ago
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    i=dq/dt dq=i(dt) integrate to get the charge use charge=capacitance*voltage

  2. anonymous
    • 5 years ago
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    i=C dv/dt

  3. anonymous
    • 5 years ago
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    therefore 4 dv/dt = 5e^(-t/2)

  4. anonymous
    • 5 years ago
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    so \[\frac{dv}{dt} = \frac{5}{4}e^{-\frac{t}{2}}\]

  5. anonymous
    • 5 years ago
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    integrate both sides with respect to t

  6. anonymous
    • 5 years ago
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    \[v = -\frac{5}{2}e^{-\frac{t}{2}} +C \]

  7. anonymous
    • 5 years ago
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    now, it is initially uncharged, so when t=0, v=0 that gives the constant C = 5/2 \[v(t) = \frac{5}{2} ( 1 - e^{-\frac{t}{2}}) V \]

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