Final answer:
To find the steady-state current in the RLC circuit, calculate the impedance of the circuit using the given values of resistance, inductance, and capacitance. Then, use Ohm's law to find the current by plugging in the impedance and the voltage in the circuit.
Step-by-step explanation:
To find the steady-state current in the RLC circuit, we need to calculate the impedance of the circuit and then use Ohm's law to find the current. The impedance of the circuit, Z, is given by the formula:
Z = sqrt(R^2 + (XL - XC)^2)
Where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance. In this circuit, R = 0.2Ω, XL = ωL = 314*0.1 = 31.4Ω, and XC = 1/(ωC) = 1/(314*2) = 0.0016Ω. Plugging these values into the formula, we get:
Z = sqrt((0.2)^2 + (31.4 - 0.0016)^2) = 31.4Ω
Now we can use Ohm's law, V = IZ, where V is the voltage and I is the current. The voltage in the circuit is given by E = 220sin(314t) V. The steady-state current can be found by replacing V with E in Ohm's law:
E = IZ => 220sin(314t) = 31.4I => I = (220sin(314t)) / 31.4