LR Derivations
Rising and Decaying
Derivations
Use the formulas below to drive the following equations.
Rise of Current
- Switch is flipped to position "a".
- Derive the current in the circuit as a function of time, i(t).
Step it Out.
1. Use Kirchhoff's Loop Rule:
- One Gain
- Two Drops
- Sums to Zero
3. Should arrive at the integral shown (right or below).
4. Integrate and evaluate.
5. Rearrange and solve for "i".
6. Final equation shown below.Decay of Current
1. After the current has reached a steady state the switch is moved to position "b".
2. Derive the current in the circuit as a function of time, i(t).
Step it Out.
1. Use Kirchhoff's Loop Rule.
- One Gain (What's the gain?)
- One Drop
- Sums to Zero
- Is di/dt a decreasing or increasing rate?
3. Should arrive at the integral shown (right or below).
4. Integrate and evaluate.
5. Rearrange and solve for "i".6. Final equation shown below.
David Carroll
www.GravityKills.net