Answer:
14.488 amperes
Step-by-step explanation:
The amplitude I of the current is given by
[tex]\large I=\displaystyle\frac{E_m}{Z}[/tex]
where
[tex]\large E_m[/tex] = amplitude of the energy source E(t).
Z = Total impedance.
The amplitude of the energy source is 120, the maximum value of E(t)
The total impedance is given by
[tex]\large Z=\sqrt{R^2+(X_L-X_C)^2}[/tex]
where
R= Resistance
L = Inductance
C = Capacitance
w = Angular frequency
[tex]\large X_L=wL[/tex] = inductive reactance
[tex]\large X_C=\displaystyle\frac{1}{wC}[/tex] = capacitive reactance
As E(t) = 120sin(12t), the angular frequency w=12
So
[tex]\large X_L=12*0.37=4.44\\\\X_C=1/(12*7)=0.012[/tex]
and
[tex]\large Z=\sqrt{7^2+(4.44-0.012)^2}=8.283[/tex]
Finally
[tex]\large I=\displaystyle\frac{E_m}{Z}=\frac{120}{8.283}=14.488\;amperes[/tex]
