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
RLC Circuits and Phasors
Practice!
| Practice 11.3.1 |
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Consider the voltage phasors shown at three instants of time. Choose the figure that represents the instant of time at which the instantaneous value of the voltage has the largest magnitude. |
| Practice 11.3.2 |
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| Consider the voltage phasors shown at three instants of time. Choose the figure that represents the instant of time at which the instantaneous value of the voltage has the smallest magnitude. |
Impedance
Practice!
| Practice 11.3.3 |
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A resistor with resistance R and a capacitor with capacitance C are connected in series with an AC source that provides a sinusoidal voltage of  , where V is the maximum voltage,  is the angular frequency, and t is the time. What happens to the rms current through the resistor as the angular frequency of the AC is increased? |
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.
| Practice 11.3.4 |
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| A resistor with resistance R and an inductor with inductance L are connected in series with an AC source that provides a sinusoidal voltage of , where V is the maximum voltage, is the angular frequency, and t is the time. What happens to the rms current through the resistor as the angular frequency of the AC is increased? |
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.
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