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    Charging Discharging A Capacitor

    Uploaded by

    Mr Sonu
    1) Charging a capacitor involves an exponential increase in charge (q) and exponential decrease in current (i) over time with a characteristic time constant (RC) determined by the resistor (R) and capacitor (C) values. 2) Discharging a capacitor involves an exponential decrease in charge (q) and exponential decrease in current (i) over time with the same characteristic time constant (RC). 3) The time constant (RC) represents the time required for the charge/current to reach approximately 63% of its maximum/initial value during charging/discharging.

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    Charging Discharging A Capacitor

    Uploaded by

    Mr Sonu
    31 views2 pages
    1) Charging a capacitor involves an exponential increase in charge (q) and exponential decrease in current (i) over time with a characteristic time constant (RC) determined by the resistor (R) and capacitor (C) values. 2) Discharging a capacitor involves an exponential decrease in charge (q) and exponential decrease in current (i) over time with the same characteristic time constant (RC). 3) The time constant (RC) represents the time required for the charge/current to reach approximately 63% of its maximum/initial value during charging/discharging.

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    Charging Discharging a Capacitor

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    1) Charging a capacitor involves an exponential increase in charge (q) and exponential decrease in current (i) over time with a characteristic time constant (RC) determined by the resistor (R) and capacitor (C) values. 2) Discharging a capacitor involves an exponential decrease in charge (q) and exponential decrease in current (i) over time with the same characteristic time constant (RC). 3) The time constant (RC) represents the time required for the charge/current to reach approximately 63% of its maximum/initial value during charging/discharging.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    31 views2 pages

    Charging Discharging A Capacitor

    Uploaded by

    Mr Sonu
    1) Charging a capacitor involves an exponential increase in charge (q) and exponential decrease in current (i) over time with a characteristic time constant (RC) determined by the resistor (R) and capacitor (C) values. 2) Discharging a capacitor involves an exponential decrease in charge (q) and exponential decrease in current (i) over time with the same characteristic time constant (RC). 3) The time constant (RC) represents the time required for the charge/current to reach approximately 63% of its maximum/initial value during charging/discharging.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 2

    Charging a Capacitor

    𝐸 = 𝑉𝐶 + 𝑉𝑅
    r 𝑞
    = + 𝐼𝑅
    𝐶
    𝑞 𝑑𝑞
    = + 𝑅
    𝐶 𝑑𝑡
    𝑑𝑞 𝑞
    𝑜𝑟 𝑅 + =𝐸
    𝑑𝑡 𝐶
    𝑑𝑞 𝑑𝑡
    𝑜𝑟 =
    𝐸𝐶−𝑞 𝑅𝐶
    Integrating both sides
    𝑞 𝑑𝑞 1 𝑡
    ‫׬‬0 = ‫𝑡𝑑 ׬‬
    𝐸𝐶−𝑞 𝑅𝐶 0
    𝑡
    𝑜𝑟 𝑞 = 𝐸𝐶 1 − 𝑒 −𝑅𝐶
    𝑡
    −
    = 𝑞0 1 − 𝑒 𝑅𝐶

    Where q0 = EC = maximum charge stored in the capacitor.


    Differentiating
    𝑡
    𝑑𝑞
    𝑖 = = 𝑖0𝑒 −𝑅𝐶
    𝑑𝑡
    The potential across the capacitor
    𝑡
    𝑞
    𝑉𝐶 = = 𝐸 1 − 𝑒 −𝑅𝐶
    𝐶
    The potential across the resistor
    𝑡
    𝑉𝑅 = 𝑖𝑅 = 𝐸𝑒 −𝑅𝐶
    𝐼 = 𝑒 −1 𝐼0 = 0.37𝑖0
    and 𝑞 = 𝑞0 1 − 𝑒 −1 = 0.63𝑞0
    RC has the dimension of time, is called time constant in
    which the charge increases to 0.638 times the
    1
    equilibrium charge, and the current decreases to
    𝑒
    times the equilibrium current.
    Discharging a Capacitor
    r

    0 = 𝑉𝑅 + 𝑉𝐶
    𝑞
    = 𝐼𝑅 +
    𝐶
    𝑑𝑞 𝑞
    𝑜𝑟 𝑅 + =0
    𝑑𝑡 𝐶
    𝑞 𝑑𝑞 1 𝑡
    𝑜𝑟 ‫𝑞 𝑞׬‬ =− ‫𝑡𝑑 ׬‬
    0 𝑅𝐶 0
    𝑡
    𝑜𝑟 𝑞 = 𝑞0𝑒 𝑅𝑐

    Instantaneous current
    𝑑𝑞
    𝐼=
    𝑑𝑡
    𝑡
    −𝑅𝐶
    = −𝐼0𝑒
    When t = RC, q = q0/e = 0.37q0
    t = RC is the time in which the charge
    decreases to 0.37 times the
    maximum charge q0.

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