Question

a capacitor, a resistor and a 40mH inductor are connected in series to an a.C source of frequency 60 Hz. calculate the capacitance of the capacitor, if current is in the same phase with the voltage.

Answer 1

$$\begin{gathered} Ifthea.c.currentandvoltageareinthesamephasethencircuitisresistorcircuitonly \\ itmeanscircuitisresonantLCRa.c.circuiti.e. \\ {X}_L=X_C \\ OR\omega L=\frac{1}{\omega C} \\ ORC=\frac{1}{{\omega }^{2}L}=\frac{1}{4{\pi }^2{\upsilon }^{2}L} \\ ORC=\frac{1\times 7\times 7}{4\times 22\times 22\times 60\times 60\times 40\times {10}^{-3}}=\frac{49}{88\times 144\times 22}==1.73\times {10}^{-4}f=173\mu f. \end{gathered}$$