Q factor is defined as the ratio of

Explanation:

Q Factor (Quality Factor)

Definition: The Q factor, or Quality Factor, is a dimensionless parameter that describes the damping or energy loss of an oscillatory system. In the context of electrical circuits, it quantifies the sharpness of the resonance of a circuit and is defined as the ratio of the energy stored in the reactive components (inductors or capacitors) to the energy dissipated per cycle in the resistive elements.

Correct Option Analysis:

The correct option is:

Option 1: Resistance / inductance of reactive element.

The Q factor is defined as:

Q = (Energy stored in the reactive element) / (Energy dissipated per cycle)

For a series RLC circuit, the Q factor can be expressed in terms of the inductance (L) and resistance (R). The formula is:

Q = ωL / R

Where:

• ω = 2πf, the angular frequency of the circuit.
• L = Inductance of the inductor.
• R = Resistance of the circuit.

This equation shows that the Q factor is directly proportional to the inductance and inversely proportional to the resistance of the circuit. A higher Q factor indicates lower energy loss and sharper resonance, which is desirable in many practical applications such as communication systems and filters.

Therefore, the Q factor is essentially the ratio of resistance (R) to the inductance (L) of the reactive element when we consider the relationship between energy dissipation and energy storage in the circuit.

Additional Information

Analysis of Other Options:

Option 2: Resistance / capacitance of reactive element.

This option is incorrect because the Q factor is not defined in terms of capacitance (C) alone. While capacitance is a reactive element, the Q factor depends on the ratio of stored energy to dissipated energy, which is more commonly expressed in terms of inductance (L) and resistance (R) in a series RLC circuit. In circuits where capacitance is the primary reactive element, the Q factor is defined using the reciprocal of capacitance (1/C), not capacitance directly.

Option 3: Resistance to reactance of reactive element.

This option is also incorrect because the Q factor is not directly defined as the ratio of resistance (R) to reactance (X). Instead, the Q factor is related to the ratio of reactance (X) to resistance (R) in a series circuit, as reactance determines the energy storage in the reactive elements. Specifically, for an inductor:

Q = X_L / R = ωL / R

For a capacitor:

Q = X_C / R = 1 / (ωCR)

Thus, the Q factor is inversely proportional to resistance and directly proportional to the reactance.

Option 4: Resistance to susceptance of reactive element.

This option is incorrect because susceptance (B) is the reciprocal of reactance (1/X), which is used in the analysis of parallel circuits. The Q factor is not defined in terms of resistance (R) to susceptance (B). The relationship between susceptance and Q factor is more relevant for parallel RLC circuits, but even in those cases, the Q factor is not expressed as the ratio of resistance to susceptance.

Conclusion:

The correct definition of the Q factor involves the ratio of resistance (R) to the inductance (L) of the reactive element, as given in Option 1. The Q factor plays a critical role in determining the performance of resonant circuits, with higher Q values indicating better performance due to lower energy losses. Understanding the Q factor and its mathematical relationship with circuit parameters is essential for designing efficient electrical systems, especially in applications requiring high selectivity and minimal energy dissipation.