Capacitors, series and parallel combination, parallel plate capacitor with/without dielectric
- The plates of a parallel plate capacitor are separated by d. Two slabs of different dielectric constant K_1 and K_2 with thickness 3/8d and d/2, respectively are inserted in the capacitor. Due to this, the capacitance becomes two times larger than wh… Answer: 1. 2.66 Key idea: for slabs inserted in a capacitor, C=ε₀A/d-t₁-t₂+t₁/K₁+t₂/K₂ . Here t₁=3/8d , t₂=1/2d , and C=2C₀ , so the denomin... 1
- If the plates of a parallel plate capacitor connected to a battery are moved close to each other, thenA. the charge stored in it, increases.B. the energy stored in it, decreases.C. its capacitance increases.D. the ratio of charge to its potential rem… Answer: 3. A, C and E only Key idea: The capacitor stays connected to the battery, so the voltage V stays fixed. Moving the plates closer re... 1
- In the following circuit, the equivalent capacitance between terminal A and terminal B is : Answer: 2. 2 μ F Key idea: The circuit is symmetric, so the middle capacitor is part of a balanced bridge and holds no charge. Let M be the... 1
- The equivalent capacitance of the system shown in the following circuit is : Answer: 2. 2 μ F From the figure, one 3 μ F capacitor is in series with a parallel pair of 3 μ F capacitors. Parallel pair: 3+3=6 μ F. Serie... 1
- The equivalent capacitance of the combination shown in the figure is : Answer: 2. 2C Key idea: wires joining the two sides short-circuit a capacitor, and the rest become parallel. The right-hand vertical wire jo... 1
- The capacitance of a parallel plate capacitor with air as medium is 6 μF. With the introduction of a dielectric medium, the capacitance becomes 30 μF. The permittivity of the medium is :(ε_0 = 8.85×10^-12 C^2 N^-1 m^-2) Answer: 3. 0.44×10⁻¹⁰ C ² N ⁻¹ m ⁻² Capacitance with a dielectric of relative permittivity K is C=KC₀ . So K=30/6=5 Permittivity of the medi... 1
- The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is Answer: 1. independent of the distance between the plates. The field of one plate is σ/2ε₀ , and this acts on the charge Q of the other plat... 1
- A parallel-plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials having dielectric constants k_1,k_2,k_3 and k_4 as shown in the figure below. If a single dielectric material is to be used to have th… Answer: 2. 2/k=3/k₁+k₂+k₃+1/k₄ The upper half (thickness d/2 ) has three dielectrics side by side, each of area A/3 , so they are in paralle... 1