Respuesta :
Answer:
(a) The impedance in the circuit is [tex]Z=183.33\Omega[/tex].
(b)The resistance is [tex]R=38.89\Omega[/tex].
(c) The inuctance is 0.57 H.
Explanation:
(a)
The expression for the impedance is as follows:
[tex]Z=\frac{V_rms}{I_rms}[/tex]
Here, [tex]V_rms[/tex] is the rms voltage and [tex]I_rms[/tex] is the rms current.
Put[tex]V_rms=110 V[/tex] and [tex]I_rms=0.600 A[/tex].
[tex]Z=\frac{110}{0.600}[/tex]
[tex]Z=183.33\Omega[/tex]
Therefore, the impedance in the circuit is [tex]Z=183.33\Omega[/tex].
(b)
The expression for the average power is as follows;
[tex]P_{a}=I_{rms}^{2}R[/tex]
Here, [tex]P_{a}[/tex] is the average power and R is the resistance.
Calculate the resistance by rearranging the above expression.
[tex]R=\frac{P_{a}}{I_{rms}^{2}}[/tex]
Put [tex]P_{a}=14W[/tex] and
[tex]R=\frac{14}{{0.600}^{2}}[/tex]
[tex]R=38.89\Omega[/tex]
Therefore, the resistance is [tex]R=38.89\Omega[/tex].
(c)
The expression for the impedance is as follows;
[tex]Z^{2}=R^{2}+X_{L}^{2}[/tex]
Here,[tex]X_{L}[/tex] is the inductive reactance.
Put [tex]Z=183.33\Omega[/tex] and [tex]R=38.89\Omega[/tex].
[tex](183.33)^{2}=(38.89)^{2}+X_{L}^{2}[/tex]
[tex]X_{L}=179.16\Omega[/tex]
The expression for the inductive reactance in terms of frequency is as follows;
[tex]X_{L}=2\pi fL[/tex]
Here, L is the inductance.
Calculate the inductance by rearranging the above expression.
[tex]L=\frac{X_{L}}{2\pi f}[/tex]
Put [tex]X_{L}=179.16\Omega[/tex] and f=50Hz.
[tex]L=\frac{179.16}{2\pi (50)}[/tex]
L=0.57 H
Therefore, the inuctance is 0.57 H.
