Solved examples of energy stored in an inductor with varying inductance

📚 Quick Study Guide

• 🧲 An inductor stores energy in its magnetic field when current flows through it.
• ⚡ The energy stored in an inductor is given by the formula: $E = \frac{1}{2}LI^2$, where $E$ is the energy in Joules, $L$ is the inductance in Henries, and $I$ is the current in Amperes.
• 🔄 If the inductance $L$ varies with time or some other parameter, the energy stored will also change accordingly.
• 💡 For varying inductance, you may need to integrate to find the total energy stored or consider the instantaneous energy at a specific inductance value.
• 📏 Remember to use consistent units (Henries for inductance, Amperes for current) to obtain the energy in Joules.

Practice Quiz

1. Question 1: An inductor has an inductance of 2 H and carries a current of 3 A. What is the energy stored in the inductor?
   1. 18 J
   2. 9 J
   3. 6 J
   4. 3 J
2. Question 2: If the current through a 4 H inductor is doubled, by what factor does the stored energy increase?
   1. 2
   2. 4
   3. 8
   4. 16
3. Question 3: An inductor's inductance changes from 1 H to 3 H while the current remains constant at 2 A. What is the change in stored energy?
   1. 2 J
   2. 4 J
   3. 6 J
   4. 8 J
4. Question 4: The energy stored in a 5 H inductor is 25 J. What is the current flowing through it?
   1. 1 A
   2. \(\sqrt{2}\) A
   3. \(\sqrt{5}\) A
   4. \(\sqrt{10}\) A
5. Question 5: An inductor has an initial inductance $L_1$ and a final inductance $L_2$. If the current $I$ is constant, the ratio of final energy $E_2$ to initial energy $E_1$ is:
   1. $L_1/L_2$
   2. $L_2/L_1$
   3. $(L_1/L_2)^2$
   4. $(L_2/L_1)^2$
6. Question 6: An inductor's inductance decreases by 50% while the current increases by 50%. What is the percentage change in stored energy?
   1. Decreases by 25%
   2. Increases by 25%
   3. No change
   4. Increases by 12.5%
7. Question 7: An inductor has inductance $L(t) = 2t + 1$ (in Henries) where $t$ is time in seconds. If a constant current of 1 A flows through it, what is the energy stored at $t = 2$ seconds?
   1. 2 J
   2. 2.5 J
   3. 4 J
   4. 5 J