Respuesta :
Explanation:
Given that,
Resistance R = 75.0 ohms
Inductance L = 55.0 mH
Capacitance [tex]C = 25.0\ \mu C[/tex]
Voltage V = 12.0 V
Frequency f = 60.0 Hz
We need to calculate the angular frequency
Using formula of angular frequency
[tex]\omega = 2\pi f[/tex]
Put the value into the formula
[tex]\omega =2\times3.14\times60.0[/tex]
[tex]\omega=376.8\ rad/s[/tex]
(a). We need to calculate the value of [tex]X_{L}[/tex]
Using formula of [tex]X_{L}[/tex]
[tex]X_{L}=\omega\times L[/tex]
Put the value into the formula
[tex]X_{L}=376.8\times55.0\times10^{-3}[/tex]
[tex]X_{L}=20.724\ \Omega[/tex]
(b). We need to calculate the value of [tex]X_{L}[/tex]
Using formula of [tex]X_{C}[/tex]
[tex]X_{C}=\dfrac{1}{\omega C}[/tex]
[tex]X_{C}=\dfrac{1}{376.8\times25.0\times10^{-6}}[/tex]
[tex]X_{C}=106.16\ \Omega[/tex]
(c). We need to calculate the value of Z
Using formula of impedance
[tex]Z=\sqrt{R^2+(X_{L}-X_{C})^2}[/tex]
Put the value into the formula
[tex]Z=\sqrt{75.0^2+(20.724-106.16)^2}[/tex]
[tex]Z=113.68\ \Omega[/tex]
(d). We need to calculate the rms current
Firstly we need to calculate the current
Using formula of current
[tex]I=\dfrac{V}{R}[/tex]
Put the value into the formula
[tex]I=\dfrac{12.0}{75.0}[/tex]
[tex]I=0.16\ A[/tex]
Using formula of rms current
[tex]I_{rms}=\dfrac{I_{0}}{\sqrt{2}}[/tex]
[tex]I_{rms}=\dfrac{0.16}{\sqrt{2}}[/tex]
[tex]I_{rms}=0.113\ A[/tex]
(e). We need to calculate the rms voltage across the resistor
Using formula of rms voltage
[tex]V_{rms}=I_{rms}\times R[/tex]
[tex]V_{rms}=0.113\times75.0[/tex]
[tex]V_{rms}=8.475\ V[/tex]
(f). We need to calculate the rms voltage across the inductor
Using formula of rms voltage
[tex]V_{rms}=I_{rms}\times X_{L}[/tex]
[tex]V_{rms}=0.113\times20.724[/tex]
[tex]V_{rms}=2.342\ V[/tex]
(g). We need to calculate the rms voltage across the capacitor
Using formula of rms voltage
[tex]V_{rms}=I_{rms}\times X_{C}[/tex]
[tex]V_{rms}=0.113\times106.16[/tex]
[tex]V_{rms}=11.99\ V[/tex]
(h). We need to calculate the dissipated power by the circuit
Using formula of dissipated power
[tex]P=RI^2[/tex]
Put the value into the formula
[tex]P=75.0\times0.113^2[/tex]
[tex]P=0.958\ W[/tex]
Hence, This is the required solution.
