To increase the resonant frequency in a series-tuned circuit, what must be done to the inductance?

In a series-tuned circuit, the resonant frequency is determined by the relationship between inductance and capacitance, as described by the formula for resonant frequency:

[ f_r = \frac{1}{2\pi\sqrt{LC}} ]

where ( f_r ) is the resonant frequency, ( L ) is the inductance, and ( C ) is the capacitance.

To increase the resonant frequency (( f_r )), it is necessary to manipulate the inductance (( L )) while holding capacitance (( C )) constant. Since the frequency is inversely proportional to the square root of the inductance, decreasing the inductance will lead to an increase in resonant frequency. This is why reducing inductance results in a higher frequency; as the inductance decreases, the sqrt(LC) term also decreases, thus increasing ( f_r ).

Therefore, to achieve the desired increase in resonant frequency while maintaining a given capacitance, the inductance must be decreased.