Mathcad Community Challenge November 2026 - Electrical Engineering - RLC Circuit
The final community challenge of 2026 has an electrical engineering theme, combining one subject from college I enjoyed (differential equations), and one that really went over my head (Bode plots). We will use an RLC circuit to explore both. (R is for resistor, L is for inductor, and C is for capacitor.)
Our RLC circuit is in series and consists of a 60 Ohm resistor, a 0.01 Henry inductor, and 100 microfarad capacitor. It has a Direct Current (DC) voltage step of 12 Volts applied at time 0.
Challenge 1: Time Domain Problem (Differential Equations)
- Write the differential equation governing the capacitor voltage for the RLC circuit.
- Compute the neper frequency, resonant frequency, and damping ratio.
- Is this circuit underdamped, critically damped, or overdamped?
Challenge 2: Graphing
Using an XY Plot or Chart Component, graph the capacitor voltage as a function of time.
Challenge 3: Frequency Domain Problem (Bode Plot)
Find the Transfer Function H(s) for this circuit assuming all initial conditions are 0. Construct the Bode plot for magnitude in decibels and phase in degrees as a function of frequency.
Challenge 4: Varying Inputs
Use any Mathcad Input Controls of your choice to allow users to vary any of the inputs that you choose. Consider employing conditional formatting with Input Controls for any feedback (no pun intended) that the worksheet should share with the user (for example, damping).