1
JEE Main 2021 (Online) 27th July Evening Shift
+4
-1
A simple pendulum of mass 'm', length 'l' and charge '+ q' suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be

A
$${\tan ^{ - 1}}\left[ {{q \over {mg}} \times {{{C_1}({V_2} - {V_1})} \over {({C_1} + {C_2})(d - t)}}} \right]$$
B
$${\tan ^{ - 1}}\left[ {{q \over {mg}} \times {{{C_2}({V_2} - {V_1})} \over {({C_1} + {C_2})(d - t)}}} \right]$$
C
$${\tan ^{ - 1}}\left[ {{q \over {mg}} \times {{{C_2}({V_1} + {V_2})} \over {({C_1} + {C_2})(d - t)}}} \right]$$
D
$${\tan ^{ - 1}}\left[ {{q \over {mg}} \times {{{C_1}({V_1} + {V_2})} \over {({C_1} + {C_2})(d - t)}}} \right]$$
2
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1

A capacitor of capacitance C = 1 $$\mu$$F is suddenly connected to a battery of 100 volt through a resistance R = 100 $$\Omega$$. The time taken for the capacitor to be charged to get 50 V is :

[Take ln 2 = 0.69]
A
1.44 $$\times$$ 10$$-$$4 s
B
3.33 $$\times$$ 10$$-$$4 s
C
0.69 $$\times$$ 10$$-$$4 s
D
0.30 $$\times$$ 10$$-$$4 s
3
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be :

(Given area of plate = A)

A
$${{15} \over {34}}{{K{\varepsilon _0}A} \over d}$$
B
$${{15} \over 6}{{K{\varepsilon _0}A} \over d}$$
C
$${{25} \over 6}{{K{\varepsilon _0}A} \over d}$$
D
$${9 \over 6}{{K{\varepsilon _0}A} \over d}$$
4
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
Two capacitors of capacities 2C and C are joined in parallel and charged up to potential V. The battery is removed and the capacitor of capacity C is filled completely with a medium of dielectric constant K. The potential difference across the capacitors will now be :
A
$${V \over {K + 2}}$$
B
$${V \over K}$$
C
$${{3V} \over {K + 2}}$$
D
$${{3V} \over K}$$
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