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Class 12  »  Physics  »  Electrostatic Potential and Capacitance

Combination of Capacitors Series and Parallel - UNSOLVED PRACTICE SET

Class 12

Chapter: Electrostatic Potential and Capacitance | Topic: Combination of Capacitors Series and Parallel

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Class 12

COMBINATION OF CAPACITORS SERIES AND PARALLEL - UNSOLVED PRACTICE SET

Topic: Combination of Capacitors Series and Parallel

Time: 40 mins | Marks: 30 | Difficulty: Medium

Multiple Choice Questions

Q1. When capacitors are connected in series, the equivalent capacitance is:

  1. Greater than the largest individual capacitance
  2. Less than the smallest individual capacitance
  3. Equal to the sum of individual capacitances
  4. Equal to the average of individual capacitances

Q2. When capacitors are connected in parallel, the equivalent capacitance is:

  1. Less than the smallest individual capacitance
  2. Greater than the largest individual capacitance
  3. Equal to the reciprocal of the sum of reciprocals
  4. Equal to the product of individual capacitances

Q3. In a series combination of capacitors connected to a battery:

  1. The potential difference across each capacitor is the same
  2. The charge on each capacitor is the same
  3. The energy stored in each capacitor is the same
  4. The capacitance of each capacitor is the same

Q4. In a parallel combination of capacitors connected to a battery:

  1. The charge on each capacitor is the same
  2. The potential difference across each capacitor is the same
  3. The energy stored in each capacitor is the same
  4. The equivalent capacitance is less than any individual capacitance

Q5. Two capacitors of capacitances 2 μF and 4 μF are connected in series. Their equivalent capacitance is:

  1. 6 μF
  2. 1.33 μF
  3. 8 μF
  4. 0.5 μF

Q6. Two capacitors of capacitances 3 μF and 6 μF are connected in parallel. Their equivalent capacitance is:

  1. 2 μF
  2. 9 μF
  3. 18 μF
  4. 0.5 μF

Short Answer Questions

Q7. Derive the expression for the equivalent capacitance of two capacitors connected in series.

Q8. Derive the expression for the equivalent capacitance of two capacitors connected in parallel.

Q9. Why does the equivalent capacitance decrease when capacitors are connected in series, while it increases in parallel? Explain with physical reasoning.

Q10. Three capacitors of capacitances 2 μF, 3 μF, and 6 μF are connected in series across a 12 V battery. Calculate the charge on each capacitor.

Q11. In a circuit, two capacitors are connected in parallel. One capacitor has twice the capacitance of the other. What is the ratio of charges stored on them?

Q12. A student needs a 5 μF capacitor but only has 2 μF capacitors available. How many 2 μF capacitors are needed and how should they be connected to get an equivalent capacitance of 5 μF?

Long Answer Questions

Q13. Derive the expression for the equivalent capacitance of n capacitors connected in series. Explain why the charge on each capacitor is the same in a series combination.

Q14. Derive the expression for the equivalent capacitance of n capacitors connected in parallel. Explain why the potential difference across each capacitor is the same in a parallel combination.

Q15. In a circuit, capacitors C₁ = 2 μF, C₂ = 4 μF, and C₃ = 6 μF are connected as follows: C₁ and C₂ are in parallel, and this combination is in series with C₃. The entire combination is connected to a 24 V battery.

(a) Calculate the equivalent capacitance of the circuit.

(b) Find the charge on each capacitor.

(c) Find the potential difference across each capacitor.

(d) Calculate the total energy stored in the system.

Numerical / Application-Based Problems

Q16. In a school electronics project, you need to build a capacitor network with the following capacitors: C₁ = 1 μF, C₂ = 2 μF, C₃ = 3 μF, and C₄ = 6 μF.

(a) Connect C₁ and C₂ in series. Calculate the equivalent capacitance.

(b) Connect C₃ and C₄ in parallel. Calculate the equivalent capacitance.

(c) Now connect the series combination of (a) in parallel with the parallel combination of (b). Calculate the total equivalent capacitance.

(d) If this entire network is connected to a 12 V battery, calculate the total charge stored and the total energy stored.

(e) Find the charge on each individual capacitor.

Q17. A network of five identical capacitors, each of capacitance C = 2 μF, is arranged in a bridge configuration: AB, BC, CD, DA are the four arms with capacitors, and a fifth capacitor connects A to C (diagonal). A battery of 10 V is connected across B and D.

(a) Calculate the equivalent capacitance between B and D.

(b) Find the total charge drawn from the battery.

(c) Calculate the charge on each capacitor.

(d) Find the potential difference across the diagonal capacitor (AC).

(e) If the diagonal capacitor is removed, what is the new equivalent capacitance?

Q18. In a practical circuit design, you need a variable capacitor that can provide capacitances from 1 μF to 10 μF. You have available capacitors of 1 μF, 2 μF, 3 μF, and 4 μF.

(a) Show how to connect these capacitors using switches to obtain any of the following capacitances: 1 μF, 2 μF, 3 μF, 4 μF, 5 μF, 6 μF, 7 μF, 8 μF, 9 μF, and 10 μF. Draw the circuit diagram.

(b) Calculate the equivalent capacitance when all capacitors are connected in parallel.

(c) Calculate the equivalent capacitance when all are connected in series.

(d) If the parallel combination is charged to 5 V, how much total energy is stored?


Total: 30 Marks | Time: 40 mins

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