Solve the problems please A series circuit contains a resistor with R = 120 Ohm,

Question

Solve the problems please

A series circuit contains a resistor with R = 120 Ohm, an inductor with L = 10 H, a capacitor with C = 0.001 F, and a 12 V battery. The initial charge is Q = 0.002 C and the initial current is 0. Find the charge and current at time t. Q(t) = J(t) = A series circuit consists of a resistor with R = 20 Ohm, an inductor with L = 1 H , a capacitor with C = 0.005 F, and a generator producing a voltage of E(t) = 12sin(20t). If the initial charge and current are both 0, find the charge at time t. Q(t) = A series circuit contains a resistor with R = 16 Ohm, an inductor with L = 2 H, a capacitor with C = 0.02 F, and a generator producing a voltage of E(t) = 12sin(5t). The initial charge is Q = 0.003 C and the initial current is 0. Find the charge at time t. Q(t) = C

Explanation / Answer

V = IZ

(Z = sqrt{R^2 +(X_L - X_C)^2})

(omega = 1/sqrt{LC})

(X_C = 1/omega C;;; X_L = omega L)

(Q = Q_0sin(omega t) + an^{-1}{R/(X_L - X_C)})

(I = V/Zsin(omega t) + an^{-1}{R/(X_L - X_C)})

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