2. A series RLC circuit is composed of a resistor of resistance R, an inductor of inductance L, and a capacitor of capacitance C connected in series with an alternating emf {(15) = 6m sin wt where {m is the magnitude of the emf and w is its angular frequency. It can be shown that the charge It} on the capacitor obeys the differential equation: 03% dq q . LE +133 + a 25,331th After a sufficient time for the initial transients to die away, the circuit would reach the steady state. The analytical solution to this equation in the steady state is where the impedance Z and the phase constant :35 are given by 1 2 wL l/wC' : 2 = _1 Z R + (wL MC) , Q5 tan ( R ) Differentiating q, (t) yields the steadystate current of this circuit: __m _Z To investigate the properties of this series RLC' circuit, write Python programs to i, (t) = im sin(wt 95)), im perform the following tasks: (a) Use SciPy function odeint to numerically solve the differential equation to nd the current t) in this circuit. Compare it with the analytical solution for the steadystate current i, (t) by plotting them as a function of time t on the same graph. (b) Use matplotlib module to plot the steadystate potential difference across the resistor, inductor, and capacitor together with the steadystate current i, (t) and the emf t) of this circuit as a function of time t on the same graph. (c) Use matplotlib module to plot the amplitude of the steadystate current 11m as a function of the angular frequency w for this circuit with different values of the resistance R on the same graph. Your plot should depict the behavior of this circuit near the resonance angular frequency. You should repeat the plotting in each part for different combination of the parameters in order to clearly explain the underlying physical theories