Prove that the total degeneracy for an atomic hydrogenstate having principal quantum number n is 2n2.

RLC Circuit (3) We can then write the differential equation for charge on the capacitor The solution of this differential equation is (damped harmonic oscillation!), where 25 RLC Circuit (4) If we charge the capacitor then hook it up to the circuit, we will observe a charge in the circuit that varies sinusoidally with time and while at the same time decreasing in amplitude This behavior with time is illustrated below 26 RLC Circuit (3) We can then write the differential equation for charge on the capacitor The solution of this differential equation is (damped harmonic oscillation!), where 25 Alternating Current (1) Now we consider a single loop circuit containing a capacitor, an inductor, a resistor, and a source of emf This source of emf is capable of producing a time varying voltage as opposed to the sources of emf we have studied in previous chapters We will assume that this source of emf provides a sinusoidal voltage as a function of time given by where ω is the angular frequency of the emf and V maxis the amplitude or maximum value of the emf 28 Series RLC Circuit (3) The