Question

the voltage across a 5f capacitor is 2te-³t find the current and power​

Answer 1

Answer:-

It is given that,

The capacitor, C = 5f

The voltage across the capacitor,

Vc (t) = 2te^-3t V

Determine the current flowing through capacitor.

$i_{c = } c \frac{ {dv} )c \: }{dt}$

5 d / dt [ 2te ^-3t ]

10e^-3t - 30te ^-3t

Thus, the current flowing through the capacitor is:

ic (t) = 10e^-3t -30te ^-3t A

hope it will help you....

Answer 2

Correct Question: The voltage across a 5F capacitor is $2te^{-3t}$. Find the value of current and power​.

Given:

Capacitance of Capacitor (C) = 5 F

The voltage across the capacitor (V):  $V=2te^{-3t}$

To Find:

The Current (I) and Power (P).

Solution:

→ Calculating the current (I) using the concept of Capacitance and Voltage:

→ The capacitance is the property of an electric conductor or circuit to store the energy in the form of electrical charge.

→ The capacitance of a capacitor can be defined as the ratio of the magnitude of the charge stored (ΔQ) and the magnitude of electric potential difference (ΔV) developed.

    $As\:we\:know:C=\frac{\triangle Q}{\triangle V} \\\\\therefore \triangle Q =C\triangle V\\\\\therefore I(\triangle t)=C\triangle V\\\\\therefore I=C(\frac{\triangle V}{\triangle t} )$

    $In\:the\:differential\:form:I=C(\frac{dV}{dt} )$

     $\therefore I=(5)\times(\frac{d}{dt} 2te^{-3t} )\\\\\therefore I=5[2e^{-3t} -6te^{-3t} ]Ampere\\\\Hence\: the\: current\: in\: the \:capacitor\: is\: equal \:to\:5[2e^{-3t} -6te^{-3t} ]Ampere$

→ Calculating the Power (P) using the formula:

     $As\:we\:know\:the\:that\:Power\:is\:equal\:to\:the\:product\:of\:Voltage\:and\:Current\\\\\therefore Power(P) = Voltage(V)\times Current(I)\\\\\therefore P=(2te^{-3t})\times5[2e^{-3t} -6te^{-3t} ]\\\\\therefore P=[20te^{-6t} -12t^{2} e^{-6t} ]\:W\\\\Hence\:Power\:is\:equal\:to\:[20te^{-6t} -12t^{2} e^{-6t} ]\:W$

 $Therefore the\: Current\: in\: the \:capacitor\: is\: equal \:to\:5[2e^{-3t} -6te^{-3t} ]Ampere\\\\\:and\:Power\:is\:equal\:to\:[20te^{-6t} -12t^{2} e^{-6t} ]\:Watt.$

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