A capacitor of 2mF is charged with a DC Voltage source of 100 V . There is a resistor of 1 kilo ohms in series with the capacitor. What will

Question

A capacitor of 2mF is charged with a DC Voltage source of 100 V . There is a resistor of 1 kilo ohms in series with the capacitor. What will be the time taken by the capacitor so that the voltage across the capacitor is 70 V

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King 4 years 2021-08-23T07:20:38+00:00 1 Answers 11 views 0

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  1. Nho
    0
    2021-08-23T07:21:56+00:00
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    Answer:

    t = 0.731s

    Explanation:

    In order to calculate the time that the capacitor takes to have a voltage of 70V, you use the following formula:

    V=V_oe^{-\frac{t}{RC}}           (1)

    V: final voltage across the capacitor = 70V

    Vo: initial voltage across the capacitor = 100V

    R: resistance of the resistor in the circuit = 1kΩ = 1*10^3Ω

    C: capacitance of the capacitor = 2mF = 2*10^-3F

    t: time

    You use properties of logarithms to solve the equation (1) for t:

    \frac{V}{V_o}=e^{-\frac{t}{RC}}\\\\ln(\frac{V}{V_o})=ln(e^{-\frac{t}{RC}})\\\\ln(\frac{V}{V_o})=-\frac{t}{RC}\\\\t=-RCln(\frac{V}{V_o})

    Next, you replace the values of the parameters:

    t=-(1*10^3\Omega)(2*10^{-3})ln(\frac{70V}{100V})\\\\t=0.713s

    The capacitor takes 0.731s to reache a voltage of 70V

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