The Q of the coil using series connection measurement method is given by which of the following equations?

The Q of the coil using series connection measurement method can be calculated using the following equation:

Q = 2πfL/R = 1/ 2πfCR

Where: f = frequency of the coil

L = inductance of the coil R = equivalent series resistance of the coil In this method, the inductance and equivalent series resistance of the coil are measured in series with the coil.

The inductance is typically measured using an inductance meter while the equivalent series resistance is measured using an ohmmeter.

The Q of the coil is then calculated using the above equation. The higher the Q of the coil, the greater the efficiency of the coil.

The quality factor of a series connection of two coils is equal to the product of the quality factors of the two individual coils divided by the sum of their capacitances. Mathematically, it can be written as: Qs = (Q1 * Q2) / (C1 + C2). This equation can be derived from the formula for the total impedance of a series circuit, which is equal to the sum of the individual impedances. Since the impedance of a coil is equal to the square of its quality factor divided by its capacitance, the total impedance of the series circuit is equal to the sum of the individual quality factors divided by the sum of the individual capacitances. This is the same as the equation for the quality factor of the series circuit.

If the quality factor of coil 1 is Q₁ and the quality factor of coil 2 is Q₂, the capacitance of Coil 1 is C₁ and the capacitance of Coil 2 is C₂, then the quality factor of series connection is:
\(\rm Q_s=\frac{(C_1-C_2)}{(C_1Q_1-C_2Q_2)}\)