Capacitor Combinations — Series, parallel, energy stored
Electrostatics
18
JEE Qs
8%
Hard
60
min
Master charge conservation and potential differences across elements; these are the most powerful tools for solving complex capacitor networks and redistribution problems.
🧮 Key Formulas
✅ Key Points for JEE
- 1In a series combination, the charge (Q) on each capacitor is the same, and the total voltage (V) divides across them. The equivalent capacitance (C_eq) is always less than the smallest individual capacitance.
- 2In a parallel combination, the voltage (V) across each capacitor is the same, and the total charge (Q) divides among them. The equivalent capacitance (C_eq) is always greater than the largest individual capacitance.
- 3For complex networks, identify pure series and parallel segments and simplify them step-by-step from inside out to find the equivalent capacitance.
- 4Always apply charge conservation for isolated capacitor plates or isolated sections of a circuit. This is crucial for problems involving switching or redistribution of charge.
- 5The energy stored in a capacitor is released or consumed when it discharges. Pay attention to energy loss during charge redistribution, which occurs due to heat/sparking during charge transfer.
⚠️ Common Mistakes
- ✕Confusing the rules for combining capacitors with those for resistors (e.g., adding capacitances in series instead of reciprocals).
- ✕Not conserving charge for isolated parts of a circuit, especially when switches are opened or closed, or during charge redistribution.
- ✕Incorrectly calculating the energy stored or energy loss, often by using the wrong values of Q, V, or C (e.g., using total Q with individual C).
- ✕Failing to recognize or utilize symmetry in complex capacitor networks to simplify the analysis.
📝 Practice Questions
See allQ38.A capacitor, C1 = 6μ F is charged to a potential difference of V0 = 5 V using a 5 V battery. The battery is removed and another capacitor, C2 = 12μ F is inserted in place of the battery. When the switch 'S' is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the 2025 (29 Jan Shift 2) JEE Main Previous Year Paper charges (q1 and q2) on the capacitors C1 and C2 when equilibrium condition is reached. (1) q1 = 10μC, q2 = 20μC (2) q1 = 30μC, q2 = 15μC (3) q1 = 20μC, q2 = 10μC (4) q1 = 15μC, q2 = 30μC
Q44.A point charge causes an electric flux of −2 × 104Nm2C−1 to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is : (Given ϵ0 = 8.85 × 10−12C2 N−1 m−2 ) (1) 15.7 × 10−8C (2) 17.7 × 10−8C (3) −15.7 × 10−8C (4) −17.7 × 10−8C
Q45.An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density σo . Choose the correct option from the following. (1) Potential energy and torque both are maximum. (2) Torque on dipole is zero and net force is directed away from the sheet. (3) Torque on dipole is zero and net force acts (4) Potential energy of dipole is minimum and torque towards the sheet. is zero.
Q26.An electron is made to enter symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the electric field region with a horizontal component of velocity 106 m/s. If the magnitude of the electric field between the plates is 9.1 V/cm , then the vertical component of velocity of electron is (mass of electron = 9.1 × 10−31 kg and charge of electron = 1.6 × 10−19C ) (1) 0 (2) 1 × 106 m/s (3) 16 × 106 m/s (4) 16 × 104 m/s
Q38.A line charge of length ' a ' is kept at the center of an edge BC of a cube ABCDEFGH having edge length ' 2 a ' as shown in the figure. If the density of line charge is λ C per unit length, then the total electric flux through all the faces of the cube will be . (Take, ϵ0 as the free space permittivity) (1) λa (2) λa 2ϵ0 4ϵ0 (3) λa (4) λa 16ϵ0 8ϵ0
Q44.A parallel-plate capacitor of capacitance 40μ F is connected to a 100 V power supply. Now the intermediate space between the plates is filled with a dielectric material of dielectric constant K = 2. Due to the introduction of dielectric material, the extra charge and the change in the electrostatic energy in the capacitor, respectively, are (1) 4 mC and 0.2 J (2) 8 mC and 2.0 J (3) 2 mC and 0.4 J (4) 2 mC and 0.2 J 2025 (22 Jan Shift 1) JEE Main Previous Year Paper
NCERT Chapters
- Class 12 Physics Ch 2: Electrostatic Potential and Capacitance