Answer:
power delivered [tex]P=Vi=70.72\times 0.1360=9.62W[/tex]
Explanation:
We have given [tex]\Delta V=100\ sin(1000t)[/tex]
From the equation [tex]V_{MAX}=100volt[/tex] ,[tex]\omega =1000[/tex]
We know that [tex]V_{RMS}=\frac{V_{MAX}}{\sqrt{2}}=\frac{100}{1.414}=70.7213volt[/tex]
Resistance R = 415 OHM
Capacitance [tex]C=5.35\mu F=5.35\times 10^{-6}F[/tex]
Capacvitive reactance [tex]X_C=\frac{1}{\omega C}=\frac{1}{1000\times 5.35\times 10^{-6}}=186.9158ohm[/tex]
Inductance = 0.5 H
Inductive reactance [tex]X_L=\omega L=1000\times 0.5=500ohm[/tex]
Impedance [tex]Z=\sqrt{R^2+(X_L-X_C)^2}=\sqrt{415^2+(500-186.9158)^2}=519.8525ohm[/tex]
Now current [tex]i=\frac{V}{Z}=\frac{70.72}{519.8525}=0.1360A[/tex]
So power delivered [tex]P=Vi=70.72\times 0.1360=9.62W[/tex]
