Self-inductance: induced emf and stored energy: Class 12 practice
A changing current in a coil induces emf ε = −L dI/dt. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Faraday's law
The idea behind self-inductance: induced emf and stored energy
A changing current in a coil induces emf ε = −L dI/dt. The energy stored in its magnetic field is U = ½LI².
Step-by-step method
- Find the rate of change of current ΔI/Δt.
- |ε| = L × ΔI/Δt.
- U = ½LI².
Worked example 1 (Basic)
The current in a 0.22 H coil rises from 2 A to 3 A in 0.08 s. Find the induced emf.
- |ε| = 0.22 × 1/0.08
- Answer: 2.75 V
Worked example 2 (Standard)
The current in a 0.48 H coil rises from 3 A to 12 A in 0.11 s. Find the induced emf.
- |ε| = 0.48 × 9/0.11
- Answer: 39.27 V
Worked example 3 (Challenge)
How much energy is stored in a 0.21 H coil carrying 10 A?
- U = ½ × 0.21 × 10²
- Answer: 10.5 J
Common mistakes and misconceptions
- Forgetting to divide by time
- Using I instead of I² for energy
Practice questions
- (Basic) The current in a 0.07 H coil rises from 0 A to 8 A in 0.12 s. Find the induced emf.
- (Basic) The current in a 0.07 H coil rises from 3 A to 11 A in 0.17 s. Find the induced emf.
- (Standard) The current in a 0.26 H coil rises from 0 A to 1 A in 0.05 s. Find the induced emf.
- (Standard) The current in a 0.07 H coil rises from 5 A to 13 A in 0.16 s. Find the induced emf.
- (Challenge) How much energy is stored in a 0.4 H coil carrying 2 A?
- (Challenge) How much energy is stored in a 0.4 H coil carrying 7 A?
Answer key with full working
- Q1: |ε| = 0.07 × 8/0.12 → Answer: 4.67 V
- Q2: |ε| = 0.07 × 8/0.17 → Answer: 3.29 V
- Q3: |ε| = 0.26 × 1/0.05 → Answer: 5.2 V
- Q4: |ε| = 0.07 × 8/0.16 → Answer: 3.5 V
- Q5: U = ½ × 0.4 × 2² → Answer: 0.8 J
- Q6: U = ½ × 0.4 × 7² → Answer: 9.8 J
Syllabus note
This skill is listed under "Electromagnetic Induction" for Class 12 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is self-inductance: induced emf and stored energy in?
"Electromagnetic Induction", Class 12 Physics (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.