1
JEE Main 2019 (Online) 12th April Morning Slot
+4
-1
Two identical parallel plate capacitors, of capacitance C each, have plates of area A, separated by a distance d. The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants K1, K2 and K3. The first capacitor is filled as shown in fig.I, and the second one is filled as shown in fig II. If these two modified capacitors are charged by the same potential V, the ratio of the energy stored in the two, would be (E1 refers to capacitor (I) and E2 to capacitor (II)):
A
$${{{E_1}} \over {{E_2}}} = {{\left( {{K_1} + {K_2} + {K_3}} \right)\left( {{K_2}{K_3} + {K_3}{K_1} + {K_1}{K_2}} \right)} \over {{K_1}{K_2}{K_3}}}$$
B
$${{{E_1}} \over {{E_2}}} = {{{K_1}{K_2}{K_3}} \over {\left( {{K_1} + {K_2} + {K_3}} \right)\left( {{K_2}{K_3} + {K_3}{K_1} + {K_1}{K_2}} \right)}}$$
C
$${{{E_1}} \over {{E_2}}} = {{\left( {{K_1} + {K_2} + {K_3}} \right)\left( {{K_2}{K_3} + {K_3}{K_1} + {K_1}{K_2}} \right)} \over {9{K_1}{K_2}{K_3}}}$$
D
$${{{E_1}} \over {{E_2}}} = {{9{K_1}{K_2}{K_3}} \over {\left( {{K_1} + {K_2} + {K_3}} \right)\left( {{K_2}{K_3} + {K_3}{K_1} + {K_1}{K_2}} \right)}}$$
2
JEE Main 2019 (Online) 10th April Evening Slot
+4
-1
A simple pendulum of length L is placed between the plates of a parallel plate capacitor having electric field E, as shown in figure. Its bob has mass m and charge q. The time period of the pendulum is given by :
A
$$2\pi \sqrt {{L \over {\sqrt {{g^2} - {{{q^2}{E^2}} \over {{m^2}}}} }}}$$
B
$$2\pi \sqrt {{L \over {\left( {g + {{qE} \over m}} \right)}}}$$
C
$$2\pi \sqrt {{L \over {\sqrt {{g^2} + {{{q^2}{E^2}} \over {{m^2}}}} }}}$$
D
$$2\pi \sqrt {{L \over {\left( {g - {{qE} \over m}} \right)}}}$$
3
JEE Main 2019 (Online) 10th April Morning Slot
+4
-1
Figure shows charge (q) versus voltage (V) graph for series and parallel combination of two given capacitors. The capacitances are :
A
40 $$\mu$$F and 10 $$\mu$$F
B
60 $$\mu$$F and 40 $$\mu$$F
C
20 $$\mu$$F and 30 $$\mu$$F
D
50 $$\mu$$F and 30 $$\mu$$F
4
JEE Main 2019 (Online) 9th April Evening Slot
+4
-1
The parallel combination of two air filled parallel plate capacitors of capacitance C and nC is connected to a battery of voltage, V. When the capacitors are fully charged, the battery is removed and after that a dielectric material of dielectric constant K is placed between the two plates of the first capacitor. The new potential difference of the combined system is :-
A
V
B
$${V \over {K + n}}$$
C
$${{(n+1)V} \over {K + n}}$$
D
$${{nV} \over {K + n}}$$
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