R,L,C in Series/Parallel

When resistors (R), inductors (L), and capacitors (C) are connected in series or parallel, their electrical properties combine differently.

Series Connection:
In a series connection of R, L, and C, the current flowing through each component is the same. The total impedance (Z) is the sum of the individual impedances. The impedance of a resistor is simply its resistance (R), the impedance of an inductor is jωL (where ω is the angular frequency and j is the imaginary unit), and the impedance of a capacitor is 1/(jωC). So, the total impedance Z = R + j(ωL - 1/(ωC)).

Parallel Connection:
In a parallel connection, the voltage across each component is the same. The total admittance (Y) is the sum of the individual admittances. The admittance of a resistor is 1/R, the admittance of an inductor is -j/(ωL), and the admittance of a capacitor is jωC. So, the total admittance Y = 1/R + jωC - j/(ωL).

For example, in a radio frequency circuit, understanding the series and parallel combinations of R, L, and C helps in designing filters and matching networks.

In conclusion, the behavior of R, L, and C in series and parallel connections is crucial in analyzing and designing electrical circuits for various applications.