(a) What is the time constant of this circuit? (b) Calculate the following at t

Question

(a) What is the time constant of this circuit?

(b) Calculate the following at t = 2 s

(i) How much charge is on the capacitor at t = 2 s?

(ii) What is the current in the circuit at t = 2 s?

(iii) What is the potential difference across the resistor at t = 2 s?

(iv) What is the potential difference across the capacitor at t = 2 s?

(c) Calculate the following at t = 210 s

(i) How much charge is on the capacitor at t = 210 s?

(ii) What is the current in the circuit at t = 210 s?

(iii) What is the potential difference across the resistor at t = 210 s?

(iv) What is the potential difference across the capacitor at t = 210 s?

Explanation / Answer

Given Resistance , R = 500 k Capacitance , C = 12 F Voltage , V = 10 V a) Time constant , = RC = (500 *10^3 ) *(12 *10^-6 F)                             = 6s b) i) The maximum charge on the capacitor is     qo = CV = 12*10^-6 F * 10 V = 120 C    The charge after 2 s is    q = qo (1- e-t/)       = 120 *10^-6 C ( 1 - e-2/6) = 33.7C ii) Current in the circuit is , I = Io e-t/            I = (10 V / 500k) e-2/6            [where Io = V/R]              = 1.43 *10^-5 A iii) Potential difference across the resistor is      Vr = I R = (1.43 *10^-5 A) *(500 *10^3 )           = 7.15 V iv) Potential difference across the capacitor is       Vc = V -   Vr = 10V - 7.15V             = 2.85V ----------------------------------------------------------- c) (i) The maximum charge on the capacitor is     qo = CV = 12*10^-6 F * 10 V = 120 C    The charge after 210 s is    q = qo (1- e-t/)       = 120 *10^-6 C ( 1 - e-210/6) = 1.20 *10^-4 C ii) Current in the circuit is , I = Io e-t/            I = (10 V / 500k) e-210/6            [where Io = V/R]              = 1.26 *10^-20 A iii) Potential difference across the resistor is      Vr = I R = (1.26 *10^-20 A) *(500 *10^3 )           = 6.3 *10^-15 V iv) Potential difference across the capacitor is       Vc = V -   Vr = 10V - 6.3 *10^-15 V           ˜ 10 V                 qo = CV = 12*10^-6 F * 10 V = 120 C    The charge after 210 s is    q = qo (1- e-t/)       = 120 *10^-6 C ( 1 - e-210/6) = 1.20 *10^-4 C ii) Current in the circuit is , I = Io e-t/            I = (10 V / 500k) e-210/6            [where Io = V/R]              = 1.26 *10^-20 A iii) Potential difference across the resistor is      Vr = I R = (1.26 *10^-20 A) *(500 *10^3 )           = 6.3 *10^-15 V iv) Potential difference across the capacitor is       Vc = V -   Vr = 10V - 6.3 *10^-15 V           ˜ 10 V               

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