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How to solve an RC circuit with a differential equation on a TI-89 Titanium

By E-Code · updated

Press F3, ALPHA ) for deSolve(, type y′+y/2=0 (2nd = types ′; 2 is R·C), add and from 2nd 5 Test and the start value y(0)=5, then t, y and ENTER: y=5·ℯ^(-t/2), the capacitor's voltage over time.

Step by step

  1. Pick deSolve(. F3 ALPHA ) Press F3 for Calc, then ALPHA ) for C:deSolve(.
  2. Type the circuit law. Y 2nd = + Y ÷ 2 = 0 Type y′+y/2=0, with 2nd = for ′. y is the capacitor's voltage; 2 is R·C, the time constant in seconds (2 kΩ times 1 mF).
  3. Open MATH. 2nd 5 Press 2nd, then 5. MATH is written above 5.
  4. Pick and. 8 7 Press 8 for Test, then 7 for and. It adds a start value to the equation.
  5. Start at 5 volts. Y ( 0 ) = 5 , T , Y ) Type y(0)=5, then t, y and ). The capacitor starts at 5 V at time 0; t is the time letter.
  6. Solve it. ENTER Press ENTER.
  7. Read the voltage. y = 5·ℯ^(-t/2): the voltage falls from 5 V, to about 37% of that after one time constant, 2 seconds.

What the screen shows

y = 5·ℯ^(-t/2): the voltage falls from 5 V, to about 37% of that after one time constant, 2 seconds.

Look for y=5·ℯ^(-t/2) on the screen.

Try it with the keys lit up

This guide is one of E-Code's Learn lessons. Open it on E-Code's TI-89 calculator and each key lights up in turn as you press it.

Try “Solve an RC circuit with a differential equation” on the TI-89 calculator

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