# High Q Coil

If we have a capacitor with negligible loss and a high-Q coil, the…

1) Q will be much higher if we connect the two devices in series then if we connect them in parallel.

2) Q will be much lower if we connect the two devices in series then if we connect them in parallel.

3) resonant frequency will be much higher if we connect the two devices in series rather than in parallel.

4) resonant frequency will be much lower if we connect the two devices in series rather than in parallel.

5) resonant frequency will for all practical purposes be the same regardless of whether we connect the two devices in series or in parallel.

Answer

The quality factor of a coil is by definition

$Q(L) = \omega*L/R$, where $\omega$ is the angular frequency of the current.

The quality factor of a series RLC circuit is

$Q(series) = (1/R)*\sqrt{L/C}$

The quality factor of a parallel RLC circuit is

$Q(parallel) = R*\sqrt{C/L}$

Therefore $Q(series) = 1/Q(parallel)$

and if $\omega*L/R >>1$ then $Q(series) > Q(parallel)$

Q will be much higher if we connect the two devices in series then if we connect them in parallel.

The resonant frequency for a RLC series circuit is the same with the resonant frequency for a parallel RLC circuit.

$F = 1/(2*\pi*\sqrt{L*C})$

and can be deduced from the condition of equal currents (in parallel RLC) or equal voltages (in series RLC) through L and C

$\omega*L = 1/(\omega*C)$

Therefore

Resonant frequency will for all practical purposes be the same regardless of whether we connect the two devices in series or in parallel.