Consider a circuit having a 30-volt source, switch, resistance R, capacitor 0.01 microfarad, and resistance 10 kiloOHM connected in series?

Consider a circuit having a 30-volt source, switch, resistance R, capacitor 0.01 microfarad, and resistance 10 kiloOHM connected in series when the switch in this circuit is closed. The voltage across the capacitor must rise to 6.59 volt in 0.1 ms.

Identify the value of R that should be used.

2 Answers

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  • oubaas
    Lv 7
    2 months ago
    Favorite Answer

    1-6.59/30 = e^-K

    0.780 = e^-k

    k = -ln 0.780 

    k = 0.25 = t/T

    T = t/k = 10^-4/0.25 = 4*10^-4 sec = R'*C

    R' = T/C = 4*10^-4*10^8 = 4*10^4 ohm

    R = R'-10^4 = 3*10^4 ohm (30 kohm)

  • 2 months ago

    v = v₀[1–e^(–t/τ)]

    6.59 = 30[1–e^(–0.0001/τ)]

    6.59 = 30[1–e^(–0.0001/τ)]

    1–e^(–0.0001/τ) = 0.2197

    e^(–0.0001/τ) = 0.7803

    –0.0001/τ = ln(0.7803) = –0.2481

    τ = 0.0001/0.2481 = 0.0004031 s

    RC = τ = 0.0004031

    R = 0.0004031/0.01e-6 = 40310 Ω

    added R = 40310 – 10000 = 30310 Ω

    voltage on a cap, charging

    v = v₀[1–e^(–t/τ)]

    v₀ is the battery voltage

    v is the voltage after time t

    R is resistance in ohms,

    C is capacitance in farads

    t is time in seconds

    RC = τ = time constant

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