RLC Circuit Calculator

The calculation computes various parameters of an RLC circuit, which is an electrical circuit consisting of a resistor (R), an inductor (L) and a capacitor (C). These circuits are crucial in numerous applications, including radio receivers and filters.
CalculationInputs﻿﻿R
:200.00ohm​
﻿
﻿﻿C
:1.0e-6F​
﻿
﻿﻿L
:0.001H​
﻿
﻿﻿f
:1,000.00Hz​
﻿
﻿﻿Bandwidth
:50.00Hz​
﻿
Output﻿﻿Z
:251.73ohm​
﻿
﻿﻿fres
:5,033Hz​
﻿
﻿﻿Φ
:-37.39deg​
﻿
﻿﻿Q
:100.658​
﻿
Where:
Resistance (﻿R
): The electrical resistance of the circuit, which opposes the flow of current. The units are Ohms (﻿Ω
)
Capacitance (﻿C
): The ability of the circuit to store charge, which affects how quickly it can charge and discharge in response to changes in voltage. The units are Farads (﻿F
)
Inductance (﻿L
): The property of the circuit that opposes changes in current flow, contributing to energy storage in the magnetic field. The units are Henrys (﻿H
)
Frequency (﻿f
): The rate at which the circuit operates, which influences the reactive impedance components. The units are Hertz (﻿Hz
)
Bandwidth: Denotes the frequency range around the resonant frequency where the circuit's power exceeds half its peak, reflecting its frequency selectivity. The units are Hertz (﻿Hz
)
ExplanationWhat is an RLC circuit?An RLC circuit is composed of three fundamental components: a resistor (﻿R
) which dissipates energy, an inductor (﻿L
) which stores energy in its magnetic field, and a capacitor (﻿C
) which stores energy in its electric field. The combination of these elements in a circuit allows for a variety of responses to electrical inputs, including the ability to resonate at a specific frequency.
﻿
Series RLC Circuit 
This calculator receives user input for resistance, capacitance, inductance, frequency and bandwidth of an RLC circuit. The calculator outputs the impedance, resonant frequency, phase angle and quality factor. You can visualize the workflow of the calculation provided in the toggle box below.  
💡Detailed workflow of this RLC Circuit Calculator 
Output parameters and their equationsThe outputs of this calculator are discussed below.
Impedance (﻿Z
) is the total opposition to current flow in an AC circuit and is given by:
﻿
Z=R2+(XL−XC)2where:XL=2πfL =Inductive ReactanceXC=12πfC =Capacitive ReactanceZ = \sqrt{R^2 + (X_L - X_C)^2}\\\text{where:}\\X_L = 2\pi fL\ =\text{Inductive Reactance}\\X_C = \dfrac{1}{2\pi fC}\ =\text{Capacitive Reactance}Z=R2+(XL​−XC​)2​where:XL​=2πfL =Inductive ReactanceXC​=2πfC1​ =Capacitive Reactance
Resonant Frequency (﻿fres​
) is the frequency at which the circuit's impedance is at its minimum, and where the circuit naturally oscillates with maximum amplitude. It is given by:
﻿
fres=12πLCf_{\text{res}} = \dfrac{1}{2\pi\sqrt{LC}}fres​=2πLC​1​
Phase Angle (﻿ϕ
) is the phase difference between the total voltage and current and is given by:
﻿
ϕ=arctan⁡(XL−XCR)\phi = \arctan\left(\dfrac{X_L - X_C}{R}\right)ϕ=arctan(RXL​−XC​​)
Quality Factor (﻿Q
) is a unitless parameter that quantifies the 'sharpness' of the resonance in a circuit, particularly in an RLC circuit. Resonance occurs at a specific frequency, known as the resonant frequency (﻿fres​
). The Quality Factor is a measure of how narrow or sharp this resonant peak is, and is given by:
﻿
Q=fresBandwidthQ = \dfrac{f_{\text{res}}}{\text{Bandwidth}}Q=Bandwidthfres​​
The Quality Factor can be interpreted as follows: 
A High ﻿Q
(>10) indicates a sharp, narrow peak of resonance. This means the circuit is highly selective to a narrow range of frequencies around the resonant frequency. Such circuits are good for applications like filters or oscillators where selectivity is important.
A Low ﻿Q
(<10) suggests a wider, less distinct resonance peak. This means the circuit responds to a broader range of frequencies. Such circuits are useful in applications where a wider frequency response is desirable.
Applications of RLC circuitsRLC circuits are found in a variety of applications, including:
Tuning circuits in radio transmitters and receivers.
Filters in audio and telecommunications systems.
Oscillators in signal generators and other electronic devices.
Power supply circuits for smoothing and regulation.
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ReferencesAll About Circuits. (n.d.). Series-Parallel R, L, and C. Retrieved from https://www.allaboutcircuits.com/textbook/alternating-current/chpt-5/series-parallel-r-l-and-c/
Wikipedia contributors. (n.d.). RLC circuit. In Wikipedia, The Free Encyclopedia. Retrieved from https://en.wikipedia.org/wiki/RLC_circuit
Hayt Jr., W. H., Kemmerly, J. E., & Durbin, S. M. (2018). Engineering Circuit Analysis.