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JEE Mains | PYQ

The reading of the ammeter (\( A \)) in steady state in the following circuit (assuming negligible internal resistance of the ammeter) is __________________ \( A \).

A parallel plate capacitor with plate separation \( 5 \, \text{mm} \) is charged by a battery. On introducing a mica sheet of \( 2 \, \text{mm} \) 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 _______.

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

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 ______.

A parallel plate capacitor is having separation between plates \( 0.885 \, \text{mm} \). It has a capacitance of \( 1 \, \mu\text{F} \) when the space between the plates is filled with an insulating material of resistivity \( 1 \times 10^{13} \, \Omega \text{m} \) and resistance \( 17.7 \times 10^{14} \, \Omega \). Relative permittivity of the insulating material is \( \alpha \times 10^{7} \). The value of \( \alpha \) is ______.
[Take permittivity of free space \( = 8.85 \times 10^{-12} \, \text{F/m} \)]

The stored charge in the capacitor in steady state of the following circuit is ______ \( \mu \mathrm{C} \).

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

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 \( \alpha \) is ______.

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 ______.

From the circuit given below, the capacitance between terminals \( A \) and \( B \) shown in the circuit is _______ \( \mu \text{F} \).
(take \( C_1 = C_2 = C_3 = 1 \, \mu \text{F} \) and \( C_4 = 2 \, \mu \text{F} \).)

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

A \( 5 \, \mathrm{mg} \) particle carrying a charge of \( 5\pi \times 10^{-6} \, \mathrm{C} \) is moving with velocity of \( (3\hat{\imath} + 2\hat{k}) \times 10^{-2} \, \mathrm{m\, /s} \) in a region having magnetic field \( |\vec{B}| = 0.1 \hat{k} \, \mathrm{Wb\, /m^{2}} \). It moves a distance of \( \alpha \) meter along \( \hat{k} \) when it completes \( 5 \) revolutions. The value of \( \alpha \) is ______.

Under steady state condition the potential difference across the capacitor in the circuit is ________ \( \text{V} \).