Electrical extras: parallel resistors, LC resonance & EM spectrum
Three more electronics solvers: parallel resistor networks, LC resonant circuits, and the electromagnetic spectrum relation between frequency, wavelength, and photon energy.
Multi-resistor parallel network solver
$$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots + \frac{1}{R_n}$$
Equivalent resistance of resistors in parallel; current divider follows $I_k = I_{total} \cdot R_{eq}/R_k$. Source: standard circuit theory.
| Equivalent resistance R_eq | — |
LC circuit resonant frequency & impedance
$$f_0 = \frac{1}{2\pi\sqrt{LC}}, \quad Z_L = 2\pi f_0 L = \frac{1}{2\pi f_0 C}$$
Resonant frequency of a series/parallel LC tank circuit, where inductive and capacitive reactance cancel. Source: standard circuit theory.
| Resonant frequency f₀ | — | |
| Characteristic impedance Z | — |
Electromagnetic frequency, wavelength & photon energy
$$c = f\lambda, \quad E = hf = \frac{hc}{\lambda}$$
Relation between frequency, wavelength, and photon energy for electromagnetic radiation. $c=2.998\times10^8$ m/s, $h=6.626\times10^{-34}$ J·s. Source: standard EM/quantum physics.
| Frequency | — | |
| Wavelength | — | |
| Photon energy | — |