Question 318: AC fundamentals

Question

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

Accepted Answer

$$\begin{array}{ll} 
& 	ext { At resonance, } \mathrm{f}=\frac{1}{2 \pi \sqrt{\mathrm{LC}}} \Rightarrow \mathrm{f} \propto \frac{1}{\sqrt{\mathrm{LC}}} \
	herefore \quad & \frac{\mathrm{f}^{\prime}}{\mathrm{f}}=\sqrt{\left(\frac{\mathrm{L}_1 \mathrm{C}_1}{\mathrm{~L}_2 \mathrm{C}_2}ight)}=\left(\frac{\mathrm{L} 	imes \mathrm{C}}{3 \mathrm{~L} 	imes 4 \mathrm{C}}ight)^{1 / 2}=\frac{1}{(12)^{1 / 2}} \
	herefore \quad & \frac{\mathrm{f}^{\prime}}{\mathrm{f}}=\frac{1}{2 \sqrt{3}} \Rightarrow \mathrm{f}^{\prime}=\frac{\mathrm{f}}{2 \sqrt{3}}
\end{array}$$

Answer

$\frac{\mathrm{f}}{3}$

Answer

$\frac{\mathrm{f}}{2 \sqrt{3}}$

Answer

$\mathrm{6 f}$

Answer

$\frac{\mathrm{f}}{2 \sqrt{2}}$

AC fundamentals

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

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