Q1JEE Main 2026MCQ

A parallel plate air capacitor has a capacitance C. When it is half filled as show in figure with a dielectric constant K = 5, the percentage increase in the capacitance is _________.[JEE Main 2 apr 2026 Shift 1]

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📖 Explanation

Initial capacitance $C_{i}=\;\frac{A E_{0}}{d}=C$ Final capacitance ${\text{C}}_{1}=\;{ {\text{A}} \in _{0} \times 5}/{{ {\text{d}}}/{2}}=10 {\text{C}}$ ${\text{C}}_{2}=\;{ {\text{A}} \in _{0}}/{{ {\text{d}}}/{2}}=2 {\text{C}}$ ${\text{C}}_{ {\text{f}}}=\;{ {\text{C}}_{1} {\text{C}}_{2}}/{ {\text{C}}_{1}+ {\text{C}}_{2}}=\;\frac{10 \times 2}{10+2} {\text{C}}=\;\frac{5}{3} {\text{C}}$

Q2JEE Main 2026MCQ

A parallel plate capacitor has capacitance $C$ , when there is vacuum within the parallel plates. A sheet having thickness $(\;\frac{1}{3}) ^{ rd }$ of the separation between the plates and relative permittivity $K$ is introduced between the plates. The new capacitance of the system is :

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Q3JEE Main 2026NAT

A capacitor $P$ with capacitance $10 \times 10^{-6} F$ is fully charged with a potential difference of 6.0 V and disconnected from the battery. The charged capacitor $P$ is connected across another capacitor $Q$ with capacitance $20 \times 10^{-6} F$ . The charge on capacitor $Q$ when equilibrium is established will be $\alpha \times 10^{-5} C$ (assume capacitor $Q$ does not have any charge initially), the value of $\alpha$ is $\_\_\_\_$ 。

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Q4JEE Main 2026NAT

The space between the plates of a parallel plate capacitor of capacitance C (without any dielectric) is now filled with three dielectric slabs of dielectric constants $K_1=2, K_2=3$ and $K_3=5$ (as shown in figure). If new capacitance is $\;\frac{n}{3} C$ then the value of $n$ is $\_\_\_\_$ .

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Q5JEE Main 2026MCQ

A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws $25 \%$ more charge from the battery. The dielectric constant of mica is $\_\_\_\_$

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Q6JEE Main 2026MCQ

A sphere of capacitance 100 pF is charged to a potential of 100V. Another identical undercharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is $\alpha \times 10^{-7}J$ . The value of α is ______. (combined capacitance of spheres is 200 pF).[JEE Main 6 Apr 2026 shift 2]

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📖 Explanation

${\text{Q}}_{1}= {\text{CV}}=100 \times 100 {\text{pC}}=10^{4} {\text{pC}}$ ${\text{V}}_{1}= {\text{V}}_{2}=\;{ {\text{V}}}/{2}=50$ $\epsilon _{ {\text{i}}}=\;\frac{1}{2} \times 100 \times (100)^{2} {\text{pJ}}=\epsilon$ $\epsilon _{ {\text{f}}}=2 \times \;\frac{1}{2} \times 100 \times (50)^{2}=\;\frac{\epsilon }{2}$ $\Delta \epsilon =\;\frac{\epsilon }{2}=100 \times (50)^{2} {\text{pJ}}$ $=25 \times 10^{4} \times 10^{-12}=2.5 \times 10^{-7}$

Q7JEE Main 2026MCQ

A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed v. If x is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to $x^{\alpha }$ , where α is _______.[JEE Main 4 Apr 2026 Shift 1]

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📖 Explanation

Capacitance $= {\text{C}}=\;{\epsilon _{0} {\text{A}}}/{ {\text{x}}}$ Energy stored $= {\text{U}}=\;\frac{1}{2} {\text{Cv}}^{2}$ ${\text{U}}=\;\frac{1}{2} \;{\epsilon _{0} {\text{A}}}/{ {\text{x}}} {\text{v}}^{2}$ $\;{ {\text{dU}}}/{ {\text{dt}}}=\;\frac{1}{2} \epsilon _{0} {\text{Av}}^{2} (-\;{1}/{ {\text{x}}^{2}}) \;{ {\text{dx}}}/{ {\text{dt}}}$ $\;{ {\text{dU}}}/{ {\text{dt}}} \propto \;{1}/{ {\text{x}}^{2}}$

Q8JEE Main 2026MCQ

A capacitor C is first charged fully with potential difference of $V_0$ and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L . In $t s, 25 \%$ of the initial energy in the capacitor is transferred to the inductor. The value of $t$ is $\_\_\_\_$ s.

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Q9JEE Main 2026MCQ

Three parallel plate capacitors each with area $A$ and separation $d$ are filled with two dielectric ( $k_1$ and $k_2$ ) in the following fashion. Which of the following is true? $(k_1>k_2)$

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Q10JEE Main 2026MCQ

From the circuit given below, the capacitance between terminals A and B shown in the circuit is ____μF. (take $C_1 = C_2 = C_3 = 1\mu F$ and $C_4 = 2\mu F.$ )[JEE Main 4 Apr 2026 Shift 2]

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📖 Explanation

Reduced circuit is $C_1=C_2=C_3=1\mu F$ and $C_4=2 \mu F$ So, $\Rightarrow C_{eq}=2\mu F$

Q11JEE Main 2026MCQ

Under steady state condition the potential difference across the capacitor in the circuit is____V.[JEE Main 5 April 2026 Shift 2]

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📖 Explanation

$i=\;\frac{2}{6+2}=\;\frac{1}{4} {\text{A}}$ ${\text{v}}_{ {\text{C}}}= {\text{v}}_{2 Ω}= {\text{i}} \times 2=\;\frac{1}{2} {\text{V}}=0.5 {\text{V}}$

Q12JEE Main 2026NAT

A parallel plate capacitor is having separation between plates 0.885 mm. It has a capacitance of 1μF when the space between the plates is filled with an insulating material of resistivity $1 \times 10^{13} Ω m$ and resistance $17.7 \times 10^{14} Ω.$ Relative permittivity of the insulating material is $\alpha \times 10^7.$ The value of α is _________.(Take permittivity of free space = $8.85 \times 10^{-12} {\text{F}} / {\text{m}}$ )[JEE Main 8 apr 2026 shift 2]

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📖 Explanation

${\text{RC}}=\rho {\text{K}} \in _{0}$ ${\text{K}}=\;{ {\text{RC}}}/{\rho \epsilon _{0}}=\;\frac{17.7 \times 10^{14} \times 10^{-6}}{10^{13} \times 8.85 \times 10^{-12}}=2 \times 10^{7}$

Q13JEE Main 2026MCQ

Identify the correct statements: A. Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination. B. When a dielectric medium is placed between the charged plates of a capacitor, displacement of charges cannot occur due to insulation property of dielectric. C. Increasing of area of capacitor plate or decreasing of thickness of dielectric is an alternate method to increase the capacitance. D. For a point charge, concentric spherical shells centered at the location of the charge are equipotential surfaces. Choose the correct answer from the options given below :

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Q14JEE Main 2025MCQ

Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V , its capacitance is: (in pF)

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📖 Explanation

i.e. $Q=60 \times 100 {\text{pC}}$ When new capacitance $C^{'}$ is connectedThen $Q= (C+C^{'}) V$ $\;60 \times 100= (100+C^{'}) \times 20$ $\;200=C^{'}$

Q15JEE Main 2025MCQ

Which one of the following is the correct dimensional formula for the capacitance in F ? ${\text{M}}, {\text{L}}$ , T and C stand for unit of mass, length, time and charge,

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📖 Explanation

$\;\;\text{ Energy }\;=\;\frac{Q^2}{2 C}$ $\therefore \;\; [ {\text{F}}]\;=\;{[ {\text{C}}^2]\$ }/{[ {\text{ML}}^2 {\text{T}}^{-2}]$ };= [ {\text{C}}^2 {\text{M}}^{-1} {\text{L}}^{-2} {\text{T}}^{+2}]$

Q16JEE Main 2025NAT

A parallel plate capacitor has charge $5 \times 10^{-6} {\text{C}}$ . A dielectric slab is inserted between the plates and almost fills the space between the plates. If the induced charge on one face of the slab is $4 \times 10^{-6} {\text{C}}$ then the dielectric constant of the slab is $\_\_\_\_$ .

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📖 Explanation

$\;E_{\;\text{net }\;}=E_0-E_{\;\text{\in }\;}$ $\;E_{\;\text{\in }\;}=E_0 (1-\;\frac{1}{k})$ $\;Q_{\;\text{\in }\;}=Q_0 (1-\;\frac{1}{k})$ $\;4 \times 10^{-6}=5 \times 10^{-6} (1-\;\frac{1}{k})$ $\;k=5$

Q17JEE Main 2025MCQ

A parallel-plate capacitor of capacitance $40 \mu {\text{F}}$ 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

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📖 Explanation

$\;C=40 \mu F$ $\;C^{'}= kC =80 \mu F$ $\;V=100 V$ $\;Q=C V=4 mC$ $\;Q^{'}=C^{'} V=8 mC$ $\; \therefore \;\; \;\text{ Extra charge }\;=4 mC$ $\;U_1=\;\frac{1}{2} C V^2, U_2=\;\frac{1}{2} C^{'} V^2$ $\; \Delta U\;=\;\frac{1}{2} (C^{'}-C) V^2$ $\;=\;\frac{1}{2} \times 40 \times 10^4 \times 10^{-6}$ $\;=0.2 J$

Q18JEE Main 2025MCQ

A parallel plate capacitor is filled equally (half) with two dielectrics of dielectric constants $\epsilon _1$ and $\epsilon _2$ , as shown in figures. The distance between the plates is $d$ and area of each plate is $A$ . If capacitance in first configuration and second configuration are $C_1$ and $C_2$ respectively, then $\;\frac{C_1}{C_2}$ is First ConfigurationSecond Confiquration

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📖 Explanation

$\;C=\;\frac{k \epsilon _0 A}{d}$ $\;C_1=\;\frac{\epsilon _0 A}{\frac{d}{2 \epsilon _1}+\;\frac{d}{2 \epsilon _2}}=\;\frac{\epsilon _0 A}{d} \{\;\frac{1}{\frac{\epsilon _2+\epsilon _1}{2 \epsilon _1 \epsilon _2}}\}$ $\;C_2=\;\frac{\epsilon _0}{d} (\epsilon _1 \;\frac{A}{2}+\epsilon _2 \;\frac{A}{2}) =\;\frac{\epsilon _0 A}{d} \{\;\frac{\epsilon _1}{2}+\;\frac{\epsilon _2}{2}\}$ $\;\;\frac{C_1}{C_2}=\;\frac{2 \epsilon _1 \epsilon _2}{ (\epsilon _2+\epsilon _1) \;\frac{ (\epsilon _1+\epsilon _2) }{2}}=\;\frac{4 \epsilon _1 \epsilon _2}{ (\epsilon _1+\epsilon _2) ^2}$

Q19JEE Main 2025NAT

A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A . If the rate of change of potential difference between the plates is $7 \times 10^8 {\text{V}} / {\ s}$ then the integer value of the distance between the parallel plates is ______ $\mu {\text{m}}$ . $(\;\text{ Take, }\; \epsilon _0=9 \times 10^{-12} \;{ {\text{F}}}/{ {\text{m}}}, \pi =\;\frac{22}{7})$

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📖 Explanation

$Q=c V$ $V=\;\frac{Q}{c}=\;\frac{i t}{ (\;\frac{\epsilon _0 A}{d}) }$ $d=\;\frac{\epsilon _0 \pi r^2}{i} (\;\frac{v}{t})$ Putting values $d=\;\frac{9 \times 10^{-12} \times \frac{22}{7} \times (0.1)^2}{0.15} \times (7 \times 10^8)$ $=1320 \mu m$

Q20JEE Main 2025MCQ

Identify the valid statements relevant to the given circuit at the instant when the key is closed. A. There will be no current through resistor $R$ . B. There will be maximum current in the connecting wires. C. Potential difference between the capacitor plates $A$ and $B$ is minimum. D. Charge on the capacitor plates is minimum.Choose the correct answer from the options given below:

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📖 Explanation

Capacitor behaves like closed circuit at $t=0$ and charge is zero. ${\text{A}} ✗, B ✔, C ✔, D ✔$

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