EMF, internal resistance and terminal voltage: Class 12 practice

What you should know first

• Ohm's law

The idea behind emf, internal resistance and terminal voltage

A cell of emf E and internal resistance r drives I = E/(R + r) through an external resistor R. Terminal voltage V = E − Ir. Cells in series add emfs and internal resistances.

Step-by-step method

1. Total resistance = R + r.
2. I = E/(R + r).
3. V = E − Ir = IR.

Worked example 1 (Basic)

A cell of emf 9 V and internal resistance 2 Ω drives current through 1 Ω. Find the current.

1. I = 9/(1 + 2)
2. = 3 A
3. Answer: 3 A

Worked example 2 (Standard)

For the same cell (5 V, 1.5 Ω) and 12 Ω load, find the terminal voltage.

1. I = 0.37 A
2. V = E − Ir = 4.444 V
3. Answer: 4.444 V

Worked example 3 (Challenge)

4 identical cells (6 V, 1 Ω each) are in series with 17 Ω. Find the current.

1. Total emf 24 V, internal 4 Ω
2. I = 24/(17 + 4) = 1.143 A
3. Answer: 1.143 A

Common mistakes and misconceptions

• Ignoring internal resistance
• Using E for the terminal voltage

Practice questions

1. (Basic) A cell of emf 6 V and internal resistance 1 Ω drives current through 3 Ω. Find the current.
2. (Basic) A cell of emf 2 V and internal resistance 1.5 Ω drives current through 5 Ω. Find the current.
3. (Standard) For the same cell (4 V, 1 Ω) and 18 Ω load, find the terminal voltage.
4. (Standard) For the same cell (5 V, 1 Ω) and 11 Ω load, find the terminal voltage.
5. (Challenge) 4 identical cells (10 V, 2 Ω each) are in series with 17 Ω. Find the current.
6. (Challenge) 2 identical cells (3 V, 1 Ω each) are in series with 5 Ω. Find the current.

Answer key with full working

• Q1: I = 6/(3 + 1) → = 1.5 A → Answer: 1.5 A
• Q2: I = 2/(5 + 1.5) → = 0.308 A → Answer: 0.308 A
• Q3: I = 0.211 A → V = E − Ir = 3.789 V → Answer: 3.789 V
• Q4: I = 0.417 A → V = E − Ir = 4.583 V → Answer: 4.583 V
• Q5: Total emf 40 V, internal 8 Ω → I = 40/(17 + 8) = 1.6 A → Answer: 1.6 A
• Q6: Total emf 6 V, internal 2 Ω → I = 6/(5 + 2) = 0.857 A → Answer: 0.857 A

Syllabus note

This skill is listed under "Current Electricity" 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

• Current Electricity chapter notes (Class 12)
• Wheatstone and meter bridge
• Drift velocity
• Coulomb's law numericals
• Capacitors in series and parallel
• Electric field of point charges
• Electric potential and potential energy
• All Class 12 practice

Frequently asked questions

Which chapter is emf, internal resistance and terminal voltage in?

"Current Electricity", 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.