calculating the discharging time in RC circuit !!?

I'm having a hard time to solve this question. I will really thank you for helping me.

So, the problem is I have to calculate the discharging time of a capacitor in an RC circuit.

1. If the experimental set up in the picture below has a 12V battery and a 0.22microF capacitor,

determine the time it would take for the fully charged capacitor to decrease the voltage

from 12.0V to 8.0V (switch will be in the discharging position A-C).

2. The two resistors, 100Ω and 1MΩ, in this circuit are different by orders of

magnitude. Explain why

I firstly added these two resistors up so R = 100 + 10^6 = 1000,100(ohm)

and the time constant(T) = RC = (1000,000)*(0.22* 10^-6) = 0.22

The equation for discahrging the capacitor is v = v0e^(-t/T)

hence the time(t) = -T*ln(v/v0) and I got 0.0892s. 

But I think this number is too small and I got confused. Can someone answer me these two questions? Thanks in advance!

Attachment image

1 Answer

  • 3 weeks ago
    Favorite Answer

    no reason to add the two resistors, the 100 Ω is there to just limit the current into the cap when charging. When discharging, it is out of the circuit.

    τ = RC = 1M x 0.22 µF = 0.22 sec

    v = v₀e^(–t/τ)

    8 = 12e^(–t/0.22)

    e^(–t/0.22) = 8/12 = 2/3

    –t/0.22 = ln 2/3 = -0.405

    t = 0.0892 sec

    why? the circuit designer wanted the charge time to be short compared to the discharge time. But you could use 1 MΩ for both, it would just take longer for the cap to charge up.

    voltage on a cap, discharging

    v = v₀e^(–t/τ)

    v₀ is the initial voltage on the cap

    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

    • Sorry I wanted to give you 5 stars but wrong clicked

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