32.7:
RLC Series Circuits: Impedance
In AC circuits, impedance is a combination of resistance and reactance, measured in ohms, and is represented by Z.
Recalling the phasors for the RLC circuit and applying the Pythagorean theorem, the voltage or current amplitude can be determined.
By rearranging the terms, the ratio of the voltage amplitude of the circuit to the current through the circuit can be expressed as impedance.
Recalling the phase angle equation and simplifying it gives the phase angle between the current and voltage.
Consider an RLC series circuit with a 10 ohm resistor, 200 micro-henry inductor, and 100 micro-farad capacitor, connected to a 36-volt source with a 60 hertz frequency. Determine the circuit's impedance and the phase angle.
First, identify the known and unknown quantities in the circuit.
Then, determine the resistance, inductive reactance and capacitive reactance. By substituting the known terms in the impedance equation, the impedance of the circuit can be determined.
Lastly, by substituting the known terms in the phase angle equation, the phase angle between the current and voltage can be determined.
32.7:
RLC Series Circuits: Impedance
When current flow is opposed in a DC or AC circuit, it is referred to as resistance or impedance, respectively. Impedance plays a key role in determining the performance of AC circuits. It is represented by Z, which is a combination of resistance and reactance, and depends upon the angular frequency, measured in ohms.
Thus, the magnitude of the impedance is given by the following equation,
and the phase angle is given by the following equation.
If the inductive reactance in an RLC circuit is greater than the capacitive reactance, the phase angle will point in a positive direction. If it is reversed, the circuit's phase angle will be negative.
An RLC circuit is analogous to the wheel of a car driven over a corrugated road. The regularly spaced bumps in the road drive the wheel up and down; in the same way, a voltage source increases and decreases. The shock absorber of the car acts like the resistance of the RLC circuit, damping and limiting the amplitude of the oscillation. Energy within the wheel system goes back and forth between kinetic and potential energy stored in the car spring, analogous to the shift between a maximum current, with energy stored in an inductor, and no current, with energy stored in the electric field of a capacitor. The amplitude of the wheel’s motion is at a maximum if the bumps in the road are hit at the resonant frequency.
The concept of impedance has several applications, such as bioelectrical impedance analysis (BIA), transmission lines, and electronic filters. In BIA, the impedance of the human body is measured to estimate how much fat muscle the body stores. The measured impedance is low if the body has more water, which indicates that the body has more muscles because water is mostly stored in the muscles in the human body. In contrast, a high measured impedance suggests more fat in the body.
Suggested Reading
- OpenStax. (2019). University Physics Vol. 2. [Web version], Pg 396 – 398. Retrieved fromhttps://openstax.org/books/university-physics-volume-2@8ede2ba/pages/15-3-rlc-series-circuits-with-ac