# PHYS 2212 Module 11.3

## RLC Series Circuits with AC

11.3 RLC Series Circuits with AC

### Learning Objectives

By the end of this section, you will be able to:

• Describe how the current varies in a resistor, a capacitor, and an inductor while in series with an ac power source
• Use phasors to understand the phase angle of a resistor, capacitor, and inductor ac circuit and to understand what that phase angle means
• Calculate the impedance of a circuit

Practice!

### Impedance

Practice!

As the angular frequency of the AC source is increased, the rms current in the resistor increases. The rms current will depend on the circuit’s impedance where XL is the inductive reactance and XC is the capacitive reactance. Using Ohm’s Law, the rms current is , where Vrms is the rms voltage of the AC source.

In this circuit, XL = 0 because the circuit does not contain an inductor, and . As is increased, XC decreases because the capacitive reactance is inversely proportional to . This decreasing XC results in a lower impedance, which in turn results in a greater rms current.

As the angular frequency of the AC source is increased, the rms current in the resistor decreases. The rms current will depend on the circuit’s impedance where XL is the inductive reactance and XC is the capacitive reactance. Using Ohm’s Law, the rms current is , where Vrms is the rms voltage of the AC source.

In this circuit, XC = 0 because the circuit does not contain a capacitor, and . As is increased, XL increases because the inductive reactance is proportional to . This increasing XL results in a greater impedance, which in turn results in a greater rms current.

Discuss!

A series RLC circuit has R = 400 Ω, L = 1.40 H, C = 3.9 μF. It is connected to an AC source with f = 60.0 Hz and ∆Vmax = 150 V.

(a) Determine the inductive reactance, the capacitive reactance, and the impedance of the circuit.

(b) Find the maximum current in the circuit.

(c) Find the phase angle between the current and voltage.

(d) Find the maximum voltage across each element.