Capacitors in series and parallel: Class 12 practice
Capacitors combine the opposite way to resistors: in parallel C = C₁ + C₂; in series 1/C = 1/C₁ + 1/C₂. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Fractions
- Ohm's-law style combination rules
The idea behind capacitors in series and parallel
Capacitors combine the opposite way to resistors: in parallel C = C₁ + C₂; in series 1/C = 1/C₁ + 1/C₂. Charge Q = CV and stored energy U = ½CV².
Step-by-step method
- Find the equivalent capacitance.
- Q = CV for total charge.
- In series all capacitors carry the same charge; in parallel they share the same voltage.
- U = ½CV².
Worked example 1 (Basic)
10 μF and 6 μF capacitors are connected in parallel to a 55 V supply. Find the equivalent capacitance and total charge.
- C = 10 + 6 = 16 μF
- Q = CV = 16 × 55 = 880 μC
- Answer: C = 16 μF, Q = 880 μC
Worked example 2 (Standard)
20 μF and 5 μF capacitors are connected in series across 90 V. Find the equivalent capacitance and the charge on each.
- 1/C = 1/20 + 1/5 → C = 4 μF
- Q = 4 × 90 = 360 μC on each
- Answer: C = 4 μF, Q = 360 μC
Worked example 3 (Challenge)
Find the energy stored when 20 μF and 5 μF in series are charged to 30 V.
- C = 4 μF = 4 × 10⁻⁶ F
- U = ½CV² = ½ × 4 × 10⁻⁶ × 30²
- U = 0.0018 J
- Answer: 0.0018 J
Common mistakes and misconceptions
- Using resistor rules for capacitors
- Forgetting μF → F when computing energy
Practice questions
- (Basic) 9 μF and 2 μF capacitors are connected in parallel to a 50 V supply. Find the equivalent capacitance and total charge.
- (Basic) 8 μF and 8 μF capacitors are connected in parallel to a 50 V supply. Find the equivalent capacitance and total charge.
- (Standard) 20 μF and 5 μF capacitors are connected in series across 50 V. Find the equivalent capacitance and the charge on each.
- (Standard) 6 μF and 3 μF capacitors are connected in series across 100 V. Find the equivalent capacitance and the charge on each.
- (Challenge) Find the energy stored when 6 μF and 3 μF in series are charged to 100 V.
- (Challenge) Find the energy stored when 30 μF and 15 μF in series are charged to 30 V.
Answer key with full working
- Q1: C = 9 + 2 = 11 μF → Q = CV = 11 × 50 = 550 μC → Answer: C = 11 μF, Q = 550 μC
- Q2: C = 8 + 8 = 16 μF → Q = CV = 16 × 50 = 800 μC → Answer: C = 16 μF, Q = 800 μC
- Q3: 1/C = 1/20 + 1/5 → C = 4 μF → Q = 4 × 50 = 200 μC on each → Answer: C = 4 μF, Q = 200 μC
- Q4: 1/C = 1/6 + 1/3 → C = 2 μF → Q = 2 × 100 = 200 μC on each → Answer: C = 2 μF, Q = 200 μC
- Q5: C = 2 μF = 2 × 10⁻⁶ F → U = ½CV² = ½ × 2 × 10⁻⁶ × 100² → U = 0.0100 J → Answer: 0.0100 J
- Q6: C = 10 μF = 10 × 10⁻⁶ F → U = ½CV² = ½ × 10 × 10⁻⁶ × 30² → U = 0.0045 J → Answer: 0.0045 J
Syllabus note
This skill is listed under "Electrostatic Potential and Capacitance" 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 capacitors in series and parallel in?
"Electrostatic Potential and Capacitance", 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.