Final answer:
To find the rms current in the series RLC circuit, we need to use the formula for impedance (Z) and Ohm's Law. The impedance is given by Z = sqrt((R^2) + ((X_L-X_C)^2)), where R is the resistance, X_L is the inductive reactance, and X_C is the capacitive reactance. The rms current (I) can then be calculated using Ohm's Law: I = V/Z.
Step-by-step explanation:
To find the rms current in the series RLC circuit, we need to use the formula for impedance (Z) and Ohm's Law. The impedance is given by:
Z = sqrt((R^2) + ((X_L-X_C)^2)),
where R is the resistance, X_L is the inductive reactance, and X_C is the capacitive reactance. The rms current (I) can then be calculated using Ohm's Law:
I = V/Z,
where V is the voltage amplitude.
In this case, the resistance R = 50.0 Ω, the capacitance C = 25.0 µF, and the inductance L = 0.200 H. The angular frequency (ω) is equal to 350 rad/s. Substituting these values into the equations, we can find the impedance and then the rms current in the circuit.