The LC series resonant circuit produces a resonant frequency '$f$'. If L is tripled and 'C' is increased by 3C, the resonant frequency will be

The resonant frequency of an LC series circuit is given by $f = \dfrac{1}{2\pi\sqrt{LC}}$.

Given that the inductance $L$ is tripled, the new inductance is $L' = 3L$.

The capacitance $C$ is increased by $3C$, so the new capacitance is $C' = C + 3C = 4C$.

The new resonant frequency $f'$ is given by:

$f' = \dfrac{1}{2\pi\sqrt{L'C'}}$

Substituting the values of $L'$ and $C'$:

$f' = \dfrac{1}{2\pi\sqrt{(3L)(4C)}} = \dfrac{1}{2\pi\sqrt{12LC}}$

$f' = \dfrac{1}{2\sqrt{3}} \left( \dfrac{1}{2\pi\sqrt{LC}} \right)$

$f' = \dfrac{f}{2\sqrt{3}}$

Answer: $\dfrac{f}{2\sqrt{3}}$