Examples of series in the following topics:

 shows resistors in series connected to a voltage source.
 Using Ohm's Law to Calculate Voltage Changes in Resistors in Series
 $RN (series) = R_1 + R_2 + R_3 + ... + R_N.$
 A brief introduction to series circuit and series circuit analysis, including Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL).
 Three resistors connected in series to a battery (left) and the equivalent single or series resistance (right).

 Like any other form of electrical circuitry device, capacitors can be used in series and/or in parallel within circuits.
 It is possible for a circuit to contain capacitors that are both in series and in parallel.
 The circuit shown in (a) contains C1 and C2 in series.
 This image depicts capacitors C1, C2 and so on until Cn in a series.
 Calculate the total capacitance for the capacitors connected in series and in parallel

 A combination circuit can be broken up into similar parts that are either series or parallel.
 In that case, wire resistance is in series with other resistances that are in parallel.
 A series circuit can be used to determine the total resistance of the circuit.
 Essentially, wire resistance is a series with the resistor.
 This combination of seven resistors has both series and parallel parts.

 One has to be a little careful about saying that a particular function is equal to its Fourier series since there exist piecewise continuous functions whose Fourier series diverge everywhere!
 However, here are two basic results about the convergence of such series.
 Similarly for a left derivative) then the Fourier series for $f$ converges to
 These time series are reconstructed from the spectra by inverse DFT.
 At the bottom left, we show a Gaussian time series that we will use to smooth the noisy time series by convolving it with the DFT of the noisy signal.

 For the Lyman series, $n_f = 1$ for the Balmer series, $n_f = 2$; for the Paschen series, $n_f = 3$; and so on.
 The Lyman series is entirely in the UV, while part of the Balmer series is visible with the remainder UV.
 The Paschen series and all the rest are entirely IR.
 Thus, for the Balmer series, $n_f = 2$ and $n_i = 3,4,5,6...$ .
 Balmer first devised the formula for his series alone, and it was later found to describe all the other series by using different values of $n_f$.

 When voltage sources are connected in series, their emfs and internal resistances are additive; in parallel, they stay the same.
 Usually, the cells are in series in order to produce a larger total emf .
 The disadvantage of series connections of cells in this manner, though, is that their internal resistances add.
 This represents two voltage sources connected in series with their emfs in opposition.
 A series connection of two voltage sources in the same direction.

 Radioactive decay series describe the decay of different discrete radioactive decay products as a chained series of transformations.
 Radioactive decay series, or decay chains, describe the radioactive decay of different discrete radioactive decay products as a chained series of transformations.
 Most radioactive elements do not decay directly to a stable state; rather, they undergo a series of decays until eventually a stable isotope is reached.
 This diagram provides examples of four decay series: thorium (in blue), radium (in red), actinium (in green), and neptunium (in purple).

 What we will do is construct an unknown time series' DFT by hand and inverse transform to see what the resulting time series looks like.
 In all cases the time series $h_k$ is 64 samples long.
 Next, in Figure 4.12, we show at the top an input time series consisting of a pure sinusoid (left) and the real part of its DFT.
 The real (left) and imaginary (right) parts of three length 64 time series, each associated with a Kronecker delta frequency spectrum.
 These time series are reconstructed from the spectra by inverse DFT.

 In previous Atoms we learned how an RLC series circuit, as shown in , responds to an AC voltage source.
 A series RLC circuit: a resistor, inductor and capacitor (from left).
 Distinguish behavior of RLC series circuits as large and small frequencies

 Power delivered to an RLC series AC circuit is dissipated by the resistance in the circuit, and is given as $P_{avg} = I_{rms} V_{rms} cos\phi$.
 Power delivered to an RLC series AC circuit is dissipated by the resistance alone.
 The forced but damped motion of the wheel on the car spring is analogous to an RLC series AC circuit.
 Phasor diagram for an RLC series circuit.
 Calculate the power delivered to an RLCseries AC circuit given the current and the voltage