1
JEE Main 2023 (Online) 31st January Evening Shift
Numerical
+4
-1
For the given circuit, in the steady state, $\left|\mathrm{V}_{\mathrm{B}}-\mathrm{V}_{\mathrm{D}}\right|=$ ________ V.

2
JEE Main 2023 (Online) 31st January Evening Shift
Numerical
+4
-1
Two parallel plate capacitors $C_{1}$ and $C_{2}$ each having capacitance of $10 \mu \mathrm{F}$ are individually charged by a 100 V D.C. source. Capacitor $C_{1}$ is kept connected to the source and a dielectric slab is inserted between it plates. Capacitor $\mathrm{C}_{2}$ is disconnected from the source and then a dielectric slab is inserted in it. Afterwards the capacitor $C_{1}$ is also disconnected from the source and the two capacitors are finally connected in parallel combination. The common potential of the combination will be ________ V.

(Assuming Dielectric constant $=10$ )
3
JEE Main 2023 (Online) 30th January Morning Shift
Numerical
+4
-1

A capacitor of capacitance $$900 \mu \mathrm{F}$$ is charged by a $$100 \mathrm{~V}$$ battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capacitor connected to negative plate of the charged capacitor. The loss of energy in this process is measured as $$x \times 10^{-} { }^{2} \mathrm{~J}$$. The value of $$x$$ is _____________.

4
JEE Main 2023 (Online) 25th January Evening Shift
Numerical
+4
-1

A capacitor has capacitance 5$$\mu$$F when it's parallel plates are separated by air medium of thickness d. A slab of material of dielectric constant 1.5 having area equal to that of plates but thickness $$\frac{d}{2}$$ is inserted between the plates. Capacitance of the capacitor in the presence of slab will be __________ $$\mu$$F.