RLC Circuits
Electrical analogue of the spring-mass system.
Key idea
Electrical analogue of the spring-mass system.
In depth
A series RLC circuit satisfies L q′′ + R q′ + q/C = V(t), the same form as a damped spring: inductance plays mass, resistance damping, 1/C stiffness. The resonance frequency is 1/√(LC).
Worked example
L = 1 H, C = 0.25 F, R = 0: ω = 2 rad/s.
Real-world uses
- Tuning radios and filters, and designing power supplies in electronics
Common mistake
Mixing up charge q with current i = q′.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is RLC Circuits?
Electrical analogue of the spring-mass system. It is a topic at the expert level in Differential Equations, Abstract Algebra & Applied Math.
Where is RLC Circuits used in real life?
Real-world examples: Tuning radios and filters, and designing power supplies in electronics.
What should I learn before RLC Circuits?
Make sure you are comfortable with Mechanical Vibrations, the previous topic in Differential Equations, Abstract Algebra & Applied Math.
What is a common mistake with RLC Circuits?
Mixing up charge q with current i = q′.
How can I practise RLC Circuits?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after RLC Circuits?
Move on to Laplace Transform next.
Related expert topics in Differential Equations, Abstract Algebra & Applied Math
- Exact Equations – M dx + N dy = 0 with Mᵧ = Nₓ.
- Bernoulli Equations – Substitute v = y¹⁻ⁿ to linearise.
- Runge–Kutta Methods – Higher-accuracy numerical solvers.
- Second-Order Homogeneous Equations – Use the characteristic equation.
- Undetermined Coefficients – Guess the particular solution form.
- Variation of Parameters – General method for particular solutions.