1
JEE Main 2020 (Online) 8th January Evening Slot
+4
-1
A capacitor is made of two square plates each of side 'a' making a very small angle $$\alpha$$ between them, as shown in figure. The capacitance will be close to :
A
$${{{\varepsilon _0}{a^2}} \over d}\left( {1 + {{\alpha a} \over {d}}} \right)$$
B
$${{{\varepsilon _0}{a^2}} \over d}\left( {1 - {{\alpha a} \over {4d}}} \right)$$
C
$${{{\varepsilon _0}{a^2}} \over d}\left( {1 - {{\alpha a} \over {2d}}} \right)$$
D
$${{{\varepsilon _0}{a^2}} \over d}\left( {1 - {{3\alpha a} \over {2d}}} \right)$$
2
JEE Main 2020 (Online) 8th January Morning Slot
+4
-1
Effective capacitance of parallel combination of two capacitors C1 and C2 is 10 μF. When these capacitors are individually connected to a voltage source of 1V, the energy stored in the capacitor C2 is 4 times that of C1. If these capacitors are connected in series, their effective capacitance will be :
A
4.2 μF
B
8.4 μF
C
1.6 μF
D
3.2 μF
3
JEE Main 2020 (Online) 7th January Morning Slot
+4
-1
A parallel plate capacitor has plates of area A separated by distance 'd' between them. It is filled with a dielectric which has a dielectric constant that varies as k(x) = K(1 + $$\alpha$$x) where 'x' is the distance measured from one of the plates. If (ad) << 1, the total capacitance of the system is best given by the expression :
A
$${{A{ \in _0}K} \over d}\left( {1 + {{\left( {{{\alpha d} \over 2}} \right)}^2}} \right)$$
B
$${{A{ \in _0}K} \over d}\left( {1 + {{\alpha d} \over 2}} \right)$$
C
$${{A{ \in _0}K} \over d}\left( {1 + {{{\alpha ^2}{d^2}} \over 2}} \right)$$
D
$${{A{ \in _0}K} \over d}\left( {1 + \alpha d} \right)$$
4
JEE Main 2019 (Online) 12th April Evening Slot
+4
-1
In the given circuit, the charge on 4 $$\mu$$F capacitor will be :
A
5.4 $$\mu$$C
B
9.6 $$\mu$$C
C
13.4 $$\mu$$C
D
24 $$\mu$$C
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