Question

An AC voltage of the form Δv = 90.0 sin 350t, where Δv is in volts and t is in seconds, is applied to a series RLC circuit. If R = 50.0 Ω, C = 25.0 μF, and L = 0.200 H. Find the rms current in the circuit?

Answer 1

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.