Question:
Quality factor: If R is halved keeping L, C same then Q becomes?
Quality factor: If R is halved keeping L, C same then Q becomes?
Updated On: Aug 16, 2023
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Solution and Explanation
The quality factor (Q) in a series RLC circuit is given by the formula:
Q = ωL/R,
where ω is the angular frequency, L is the inductance, and R is the resistance.
If we halve the resistance (R) while keeping the inductance (L) and capacitance (C) the same, the quality factor (Q) will change.
Let's assume that ω, L, and C remain constant.
If we halve the resistance (R), the new value of Q can be calculated as follows:
Q' = ωL/(R/2) = 2ωL/R = 2Q
Therefore, if we halve the resistance while keeping the inductance and capacitance the same, the quality factor (Q) will be doubled.
Q = ωL/R,
where ω is the angular frequency, L is the inductance, and R is the resistance.
If we halve the resistance (R) while keeping the inductance (L) and capacitance (C) the same, the quality factor (Q) will change.
Let's assume that ω, L, and C remain constant.
If we halve the resistance (R), the new value of Q can be calculated as follows:
Q' = ωL/(R/2) = 2ωL/R = 2Q
Therefore, if we halve the resistance while keeping the inductance and capacitance the same, the quality factor (Q) will be doubled.
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Concepts Used:
LCR Circuit
An LCR circuit, also known as a resonant circuit, or an RLC circuit, is an electrical circuit consist of an inductor (L), capacitor (C) and resistor (R) connected in series or parallel.
Series LCR circuit
When a constant voltage source is connected across a resistor a current is induced in it. This current has a unique direction and flows from the negative to positive terminal. Magnitude of current remains constant.
Alternating current is the current if the direction of current through this resistor changes periodically. An AC generator or AC dynamo can be used as AC voltage source.
