Question

What is the relationship between the quality factor Q and the resistance R in a RLC circuit? The smaller R is, the smaller Q and the sharper the resonance peak will be. The smaller R is, the larger Q and the sharper the resonance peak will be. The larger R is, the larger Q and the sharper the resonance peak will be. The larger R is, the smaller Q and the sharper the resonance peak will be.

Answer 1

Relationship between Q and R in an RLC circuit

For Q to be high, the bandwidth must be as small as possible or Resonant frequency must be as high as possible. But Bandwidth plays a more dominant rle as its effect is exponential while that of the resonant frequenccy is linear.

So high Q circuits will have low bandwidth, which in turn means a sharper frequency response. This can be acheived by having a low value of R since R is inveresely proportional to Q.

So for small R, the value of Q will be high and bandwidth will be low and the curve will be sharper and for high value of R, the Q will be low and the bandwidth will be high, and the curve will be flatter.