Answer:
Impedance, Z = 107 ohms
Explanation:
It is given that,
Resistance, R = 100 ohms
Inductance, [tex]L=800\ mH=800\times 10^{-3}\ H=0.8\ H[/tex]
Capacitance, [tex]C=10\ \mu F=10\times 10^{-6}\ F=10^{-5}\ F[/tex]
Frequency, f = 60 Hz
Voltage, V = 120 V
The impedance of the circuit is given by :
[tex]Z=\sqrt{R^2+(X_C-X_L)^2}[/tex]...........(1)
Where
[tex]X_C[/tex] is the capacitive reactance, [tex]X_C=\dfrac{1}{2\pi fC}[/tex]
[tex]X_C=\dfrac{1}{2\pi \times 60\times 10^{-5}}=265.65\ \Omega[/tex]
[tex]X_L[/tex] is the inductive reactance, [tex]X_L={2\pi fL}[/tex]
[tex]X_L={2\pi \times 60\times 0.8}=301.59\ \Omega[/tex]
So, equation (1) becomes :
[tex]Z=\sqrt{(100)^2+(265.65-301.59)^2}[/tex]
Z = 106.26 ohms
or
Z = 107 ohms
So, the impedance of the circuit is 107 ohms. Hence, this is the required solution.
