1
JEE Advanced 2020 Paper 2 Offline
Numerical
+4
-0
Two capacitors with capacitance values C1 = 2000 $$\pm$$ 10 pF and C2 = 3000 $$\pm$$ 15 pF are connected in series. The voltage applied across this combination is V = 5.00 $$\pm$$ 0.02 V. The percentage error in the calculation of the energy stored in this combination of capacitors is ________.
2
JEE Advanced 2019 Paper 1 Offline
Numerical
+3
-0
A parallel plate capacitor of capacitance C has spacing d between two plates having area A. The region between the plates is filled with N dielectric layers, parallel to its plates, each with thickness, $$\delta = {d \over N}$$. The dielectric constant of the mth layer is $${K_m} = K\left( {1 + {m \over N}} \right)$$. For a very large N(>103), the capacitance C is $$\alpha \left( {{{K{\varepsilon _0}A} \over {d\ln 2}}} \right)$$

The value of $$\alpha$$ will be ..................

[$$\in$$0 is the permittivity of free space.]
3
JEE Advanced 2018 Paper 1 Offline
Numerical
+3
-0
Three identical capacitors $${C_1},{C_2}$$ and $${C_3}$$ have a capacitance of $$1.0\,\mu F$$ each and they are unchanged initially. They are connected in a circuit as shown in the figure and $${C_1}$$ is then filled completely with a dielectric material of relative permittivity $${\varepsilon _r}.$$ The cell electromotive force $$\left( {emf} \right)\,\,{V_0} = 8V.$$ First the switch $${S_1}$$ is closed while the switch $${S_2}$$ is kept open. When the capacitor $${C_3}$$ is fully charged, $${S_1}$$ is opened and $${S_2}$$ is closed simultaneously. When all the capacitors reach equilibrium, the charge on $${C_3}$$ is found to be $$5\,\mu C.$$ The value of $${\varepsilon _r} =$$ _________________.

4
IIT-JEE 2010 Paper 2 Offline
Numerical
+3
-0

At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them becomes 4 V? (Take ln5 = 1.6, ln3 = 1.1)