RLC Circuits

Oscillations in RLC Circuits

a) A LC circuit has an inductance of L0 and a capacitance of C0. Another LC circuit has inductance L = nL0 and capacitance L = nL0. What is the ratio of the frequencies of oscillations between the latter and the frequency of oscillations of the first circuit?
b) An LC circuit oscillates with frequency f0, for an inductance L0 and a capacitance C0. Keeping the same value of C0, replace the coil with another one with inductance L = nL0. Determine the new resonant frequency.

The current flowing in a circuit is given by
\[ \begin{gather} i=2\sin 4t \end{gather} \]
a) The average current;
b) The rms current;

RLC Circuits

For a series RLC circuit, determine:
a) The equation for the oscillations given by the charge as a function of time q(t);
b) The solution for the equation of the circuit, in the case of subcritical damping, and the angular frequency of the oscillations.

A series RLC circuit contains a resistor with resistance R = 75 Ω, an inductor with i nductance L = 10 mH, and a capacitor with capacitance C = 0.20 μF. The initial charge stored in the capacitor is equal to q0 = 0.4 mC and the current is zero. Determine:
a) The equation of electric charge as a function of time;
b) What is the type of oscillations in this circuit;
c) The graph of charge q versus time t.