Question

An RLC circuit has a resonant frequency of 48 Hz when the circuit capacitor has a capacitance of 32mF. If the capacitor is replaced by a 128-mF capacitor, the resonant frequency will be

Answer 1

$Given\\f_{1_0}=48 Hz\\C_1=32mF\\C_2=128mF\\f_{2_0}-?\\Solution:\\f_{1_0}=\frac{1}{2\pi\sqrt{LC}}; \\L=\frac{1}{4\pi^2 f_{1_0}^2C}=\frac{1}{39.438\times 48^2 \times 32\times 10^{-6}}=0.344H; \\f_{2_0}=\frac{1}{2\pi\sqrt{LC}}=\frac{1}{2\times 3.14\sqrt{0.344\times128\times10^{-6}}}=24 Hz; \\This \;task \;can\; be \;solved\; more\; easily:\\\sqrt\frac{C_2}{C_1} =2;\;\frac{f_{1_0}}{2}=\frac{48}{2}=24Hz;\\Answer: the\; resonant\; frequency\; will\; be \;24Hz$