Explore topic-wise MCQs in Joint Entrance Exam - Main (JEE Main).

This section includes 12583 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.

6301.

What is the effective capacitance between points \[X\]and \[Y\] [CBSE PMT 1999]

A.                    \[24\mu F\]
B.                    \[18\mu F\]
C.                    \[12\mu F\]
D.                    \[6\mu F\]
Answer» E.
Discussion
6302.

A \[10\mu F\] capacitor is charged to a potential difference of \[50\ V\]and is connected to another uncharged capacitor in parallel. Now the common potential difference becomes \[20\ volt\]. The capacitance of second capacitor is                                                                       [MP PET 1999; DPMT 2000]

A.                    \[10\mu F\]
B.                                      \[20\mu F\]
C.                    \[30\mu F\]
D.                                      \[15\mu F\]
Answer» E.
Discussion
6303.

A parallel plate capacitor with air as medium between the plates has a capacitance of \[10\mu F\]. The area of capacitor is divided into two equal halves and filled with two media as shown in the figure having dielectric constant \[{{k}_{1}}=2\]and \[{{k}_{2}}=4\]. The capacitance of the system will now be [MP PMT 1987; RPET 2001]

A.                    x\[10\mu F\]
B.                    \[20\mu F\]
C.                    \[30\mu F\]
D.                    \[40\mu F\]
Answer» D.                    \[40\mu F\]
Discussion
6304.

Two condensers \[{{C}_{1}}\]and \[{{C}_{2}}\] in a circuit are joined as shown in figure. The potential of point \[A\] is \[{{V}_{1}}\] and that of \[B\] is \[{{V}_{2}}\]. The potential of point \[D\] will be              [MP PMT 1997]

A.            \[\frac{1}{2}({{V}_{1}}+{{V}_{2}})\]
B.                                      \[\frac{{{C}_{2}}{{V}_{1}}+{{C}_{1}}{{V}_{2}}}{{{C}_{1}}+{{C}_{2}}}\]
C.                    \[\frac{{{C}_{1}}{{V}_{1}}+{{C}_{2}}{{V}_{2}}}{{{C}_{1}}+{{C}_{2}}}\]
D.                                      \[\frac{{{C}_{2}}{{V}_{1}}-{{C}_{1}}{{V}_{2}}}{{{C}_{1}}+{{C}_{2}}}\]
Answer» D.                                      \[\frac{{{C}_{2}}{{V}_{1}}-{{C}_{1}}{{V}_{2}}}{{{C}_{1}}+{{C}_{2}}}\]
Discussion
6305.

 A \[10\mu F\] capacitor and a \[20\mu F\] capacitor are connected in series across a \[200\ V\] supply line. The charged capacitors are then disconnected from the line and reconnected with their positive plates together and negative plates together and no external voltage is applied. What is the potential difference across each capacitor                                [MP PET 1997]

A.            \[\frac{400}{9}\text{V}\]
B.                             \[\frac{800}{9}V\]
C.                    \[400\ V\]
D.                                      \[200\,V\]
Answer» C.                    \[400\ V\]
Discussion
6306.

Choose the incorrect statement from the following: When two identical capacitors are charged individually to different potentials and connected parallel to each other after disconnecting them from the source           [MP PET 1997]

A.                    Net charge equals the sum of initial charges
B.                    The net energy stored in the two capacitors is less than the sum of the initial individual energies
C.                    The net potential difference across them is different from the sum of the individual initial potential difference
D.                    The net potential difference across them equals the sum of the individual initial potential differences
Answer» E.
Discussion
6307.

A capacitor of capacitance \[5\mu F\] is connected as shown in the figure. The internal resistance of the cell is\[0.5\Omega \]. The amount of charge on the capacitor plate is              [MP PET 1997]

A.                                                      \[0\mu C\]
B.                    \[5\mu C\]
C.                    \[10\mu C\]
D.                    \[25\mu C\]
Answer» D.                    \[25\mu C\]
Discussion
6308.

The effective capacitance between the points \[P\] and \[Q\] of the arrangement shown in the figure is              [MP PET 1997]

A.                    \[\frac{1}{2}\mu F\]
B.                    \[1\mu F\]
C.                    \[2\mu F\]
D.                    \[1.33\mu F\]
Answer» C.                    \[2\mu F\]
Discussion
6309.

In the circuit shown here \[{{C}_{1}}=6\mu F,\ {{C}_{2}}=3\mu F\]and battery\[B=20V\]. The switch \[{{S}_{1}}\] is first closed. It is then opened and afterwards \[{{S}_{2}}\] is closed. What is the charge finally on \[{{C}_{2}}\]

A.                    \[120\mu C\]
B.                    \[80\mu C\]
C.                    \[40\mu C\]
D.                    \[20\mu C\]
Answer» D.                    \[20\mu C\]
Discussion
6310.

Four capacitors are connected as shown in the figure. Their capacities are indicated in the figure. The effective capacitance between points \[x\] and \[y\] is (in\[\mu F\])                                                                                                [RPET 1997]

A.                    \[\frac{5}{6}\]
B.                    \[\frac{7}{6}\]
C.                    \[\frac{8}{3}\]
D.                    2
Answer» D.                    2
Discussion
6311.

Three capacitors of \[2.0,\ 3.0\] and \[6.0\ \mu F\] are connected in series to a \[10V\] source. The charge on the \[3.0\mu F\] capacitor is                                                                               [MP PMT 1996; RPMT 1999; Pb. PMT 2001]

A.                    \[5\mu C\]
B.                                      \[10\mu C\]
C.                    \[12\mu C\]                  
D.            \[15\mu C\]
Answer» C.                    \[12\mu C\]                  
Discussion
6312.

100 capacitors each having a capacity of \[10\mu F\]are connected in parallel and are charged by a potential difference of \[100\,kV\]. The energy stored in the capacitors and the cost of charging them, if electrical energy costs \[108\ paise\ per\ kWh\], will be                  [MP PET 1996; DPMT 2001]

A.                    \[{{10}^{7}}\ joule\] and \[300\ paise\]
B.                    \[5\times {{10}^{6}}joule\] and\[300\ paise\]
C.                    \[5\times {{10}^{6}}joule\] and\[150\ paise\]
D.                    \[{{10}^{7}}\,joule\]and \[150\ paise\]
Answer» D.                    \[{{10}^{7}}\,joule\]and \[150\ paise\]
Discussion
6313.

Four capacitors are connected in a circuit as shown in the figure. The effective capacitance in \[\mu F\]between points A and B will be                 [MP PET 1996; Pb. PMT 2001; DPMT 2003]

A.                                                      \[\frac{28}{9}\]
B.                    4
C.                    5
D.                    18
Answer» D.                    18
Discussion
6314.

The capacitor of capacitance \[4\mu F\] and \[6\mu F\] are connected in series. A potential difference of \[500\ volts\] applied to the outer plates of the two capacitor system. Then the charge on each capacitor is numerically

A.                    \[6000\,C\]
B.                                      \[1200\ C\]
C.                    \[1200\ \mu C\]          
D.            \[6000\ \mu C\]
Answer» D.            \[6000\ \mu C\]
Discussion
6315.

Three capacitors each of \[6\mu F\] are available. The minimum and maximum capacitances which may be obtained are [MP PMT 1994]

A.                    \[6\mu F,\ 18\mu F\]
B.                                      \[3\mu F,\ 12\mu F\]
C.                    \[2\mu F,\ 12\mu F\]
D.            \[2\mu F,\ 18\mu F\]
Answer» E.
Discussion
6316.

A condenser of capacity \[{{C}_{1}}\]is charged to a potential \[{{V}_{0}}\]. The electrostatic energy stored in it is \[{{U}_{0}}\]. It is connected to another uncharged condenser of capacity \[{{C}_{2}}\] in parallel. The energy dissipated in the process is        [MP PMT 1994]

A.   \[\frac{{{C}_{2}}}{{{C}_{1}}+{{C}_{2}}}{{U}_{0}}\]
B.                             \[\frac{{{C}_{1}}}{{{C}_{1}}+{{C}_{2}}}{{U}_{0}}\]
C.              \[\left( \frac{{{C}_{1}}-{{C}_{2}}}{{{C}_{1}}+{{C}_{2}}} \right){{U}_{0}}\]   
D.   \[\frac{{{C}_{1}}{{C}_{2}}}{2({{C}_{1}}+{{C}_{2}})}{{U}_{0}}\]
Answer» B.                             \[\frac{{{C}_{1}}}{{{C}_{1}}+{{C}_{2}}}{{U}_{0}}\]
Discussion
6317.

The total capacity of the system of capacitors shown in the adjoining figure between the points \[A\] and \[B\] is [Pantnagar 1987; SCRA 1996; MP PMT 2002]

A.                                                      \[1\mu F\]
B.                    \[2\mu F\]
C.                    \[3\mu F\]
D.                    \[4\mu F\]
Answer» C.                    \[3\mu F\]
Discussion
6318.

The equivalent capacitance between \[A\] and \[B\] in the figure is\[1\mu F\]. Then the value of capacitance \[C\] is                   [MP PET 1994]

A.                    \[1.4\mu F\]
B.                    \[2.5\mu F\]
C.                    \[3.5\mu F\]
D.                    \[1.2\mu F\]
Answer» B.                    \[2.5\mu F\]
Discussion
6319.

Four capacitors are connected as shown in the equivalent capacitance between the points P and Q is                                             [MP PET 1983; MP PMT 1992; UPSEAT 1999]

A.                    \[4\mu F\]
B.                    \[\frac{1}{4}\mu F\]
C.                    \[\frac{3}{4}\mu F\]
D.                    \[\frac{4}{3}\mu F\]
Answer» E.
Discussion
6320.

Two identical parallel plate capacitors are connected in series to a battery of 100\[V\]. A dielectric slab of dielectric constant 4.0 is inserted between the plates of second capacitor.  The potential difference across the capacitors will now be respectively                                                [MP PMT 1992]

A.                    50 V, 50 V                       
B.            80 V, 20 V
C.                    20 V, 80 V                       
D.            75 V, 25 V
Answer» C.                    20 V, 80 V                       
Discussion
6321.

Two capacitors of 3pF and 6pF are connected in series and a potential difference of 5000\[V\] is applied across the combination. They are then disconnected and reconnected in parallel. The potential between the plates is [MP PMT 1992]

A.                    2250\[V\]
B.                                      2222\[V\]
C.                    \[2.25\times {{10}^{6}}V\]                                         
D.            \[1.1\times {{10}^{6}}V\]
Answer» C.                    \[2.25\times {{10}^{6}}V\]                                         
Discussion
6322.

. A capacitor \[4\mu F\]charged to 50 \[V\] is connected to another capacitor of \[2\mu F\] charged to 100 \[V\] with plates of like charges connected together. The total energy before and after connection in multiples of  \[({{10}^{-2}}J)\] is  [MP PMT 1992]

A.                    1.5 and 1.33                  
B.            1.33 and 1.5
C.                    3.0 and 2.67                  
D.            2.67 and 3.0
Answer» B.            1.33 and 1.5
Discussion
6323.

A condenser of capacitance \[10\mu F\] has been charged to 100\[volts\]. It is now connected to another uncharged condenser in parallel. The common potential becomes 40\[volts\]. The capacitance of another condenser is                                                                                            [MP PET 1992]

A.                    \[15\mu F\]
B.                                      \[5\mu F\]
C.                    \[10\mu F\]
D.                                      \[16.6\mu F\]
Answer» B.                                      \[5\mu F\]
Discussion
6324.

Minimum number of capacitors of \[2\mu F\] capacitance each required to obtain a capacitor of \[5\mu F\] will be                    [MP PET 1992]

A.                    Three
B.                                      Four
C.                    Five                                  
D.            Six
Answer» C.                    Five                                  
Discussion
6325.

Four plates of equal area \[A\]are separated by equal distances \[d\] and are arranged as shown in the figure. The equivalent capacity is

A.                     \[\frac{2{{\varepsilon }_{0}}A}{d}\]                      
B.            \[\frac{3{{\varepsilon }_{0}}A}{d}\]
C.                    \[\frac{3{{\varepsilon }_{0}}A}{d}\]
D.                                      \[\frac{{{\varepsilon }_{0}}A}{d}\]
Answer» B.            \[\frac{3{{\varepsilon }_{0}}A}{d}\]
Discussion
6326.

In the circuit shown in the figure, the potential difference across the 4.5mF capacitor is                                                        [MP PET 1992; RPET 2001; BVP 2003]

A.                    \[\frac{8}{3}\ volts\]
B.                    4 \[volts\]
C.                    6\[volts\]
D.                    8 \[volts\]
Answer» E.
Discussion
6327.

\[0.2F\]capacitor is charged to \[600\,V\]by a battery. On removing the battery, it is connected with another parallel plate condenser of 1F. The potential decreases to                                                                         [MNR 1978; MP PET 2002]

A.                                                      \[100\ volts\]
B.                                      \[120\ volts\]
C.                    \[300\ volts\]               
D.            \[600\ volts\]
Answer» B.                                      \[120\ volts\]
Discussion
6328.

A condenser having a capacity of 6mF is charged to 100 V and is then joined to an uncharged condenser of \[14\mu F\] and then removed. The ratio of the charges on 6mF  and 14mF  and the potential of 6mF will be                   [MP PMT 1991]

A.                    \[\frac{6}{14}\] and \[50\ volt\]
B.                                      \[\frac{14}{6}\] and \[30\ volt\]
C.                    \[\frac{6}{14}\] and \[30\ volt\]                               
D.            \[\frac{14}{6}\] and 0\[volt\]
Answer» D.            \[\frac{14}{6}\] and 0\[volt\]
Discussion
6329.

What is the equivalent capacitance between \[A\]and\[B\] in the given figure (all are in farad)                                   [BHU 1997]

A.            \[\frac{13}{18}F\]
B.                    \[\frac{48}{13}F\]
C.                    \[\frac{1}{31}F\]
D.                    \[\frac{240}{71}F\]
Answer» E.
Discussion
6330.

Two dielectric slabs of constant \[{{K}_{1}}\] and \[{{K}_{2}}\] have been filled in between the plates of a capacitor as shown below. What will be the capacitance of the capacitor                                                        [MNR 1985; MP PET 1999; DCE 2002]         

A.                                           \[\frac{2{{\varepsilon }_{0}}A}{2}({{K}_{1}}+{{K}_{2}})\]
B.                    \[\frac{2{{\varepsilon }_{0}}A}{2}\left( \frac{{{K}_{1}}+{{K}_{2}}}{{{K}_{1}}\times {{K}_{2}}} \right)\]
C.                    \[\frac{2{{\varepsilon }_{0}}A}{2}\left( \frac{{{K}_{1}}\times {{K}_{2}}}{{{K}_{1}}+{{K}_{2}}} \right)\]
D.                    \[\frac{2{{\varepsilon }_{0}}A}{d}\left( \frac{{{K}_{1}}\times {{K}_{2}}}{{{K}_{1}}+{{K}_{2}}} \right)\]
Answer» E.
Discussion
6331.

In the following circuit, the resultant capacitance between \[A\] and \[B\] is 1mF. Then value of \[C\] is [IIT 1977]

A.                    \[\frac{32}{11}\mu F\]
B.                    \[\frac{11}{32}\mu F\]
C.                    \[\frac{23}{32}\mu F\]
D.                    \[\frac{32}{23}\mu F\]
Answer» E.
Discussion
6332.

The resultant capacitance between \[A\] and \[B\] in the following figure is equal to

A.                    \[1\mu F\]
B.                    \[3\mu F\]
C.                    \[2\mu F\]
D.                    \[1.5\mu fF\]
Answer» B.                    \[3\mu F\]
Discussion
6333.

\[2\mu F\]capacitance has potential difference across its two terminals \[200\ volts\]. It is disconnected with battery and then another uncharged capacitance is connected in parallel to it, then P.D. becomes\[20\ volts\]. Then the capacity of another capacitance will be [CPMT 1991; DPMT 2001]

A.                    \[2\mu F\]
B.                                      \[4\mu F\]
C.                    \[18\mu F\]                  
D.            \[10\mu F\]
Answer» D.            \[10\mu F\]
Discussion
6334.

In the connections shown in the adjoining figure, the equivalent capacity between \[A\] and \[B\] will be

A.                    \[10.8\mu F\]
B.                    \[69\mu F\]
C.                    \[15\mu F\]
D.                    \[10\mu F\]
Answer» E.
Discussion
6335.

A capacitor having capacitance  \[C\] is charged to a voltage \[V\]. It is then removed and connected in parallel with another identical capacitor which is uncharged. The new charge on each capacitor is now                              [MP PET 1990]

A.            CV 
B.            CV / 2
C.                    2 CV                                 
D.            CV / 4
Answer» C.                    2 CV                                 
Discussion
6336.

A \[4\mu F\]condenser is connected in parallel to another condenser of\[8\mu F\]. Both the condensers are then connected in series with a \[12\mu F\] condenser and charged to \[20\ volts\]. The charge on the plate of \[4\mu F\]condenser is                                                               [MP PET 1989]

A.                    \[3.3\mu C\]
B.                                      \[40\mu C\]
C.                    \[80\mu C\]                  
D.            \[240\mu C\]
Answer» C.                    \[80\mu C\]                  
Discussion
6337.

Three identical capacitors are combined differently. For the same voltage to each combination, the one that stores the greatest energy is                                             [MP PMT 1995]

A.                    Two in parallel and the third in series with it
B.                    Three in series
C.                    Three in parallel
D.                    Two in series and third in parallel with it
Answer» D.                    Two in series and third in parallel with it
Discussion
6338.

In the adjoining figure, four capacitors are shown with their respective capacities and the P.D. applied. The charge and the P.D. across the \[4\mu F\] capacitor will be

A.            \[600\mu C;\ 150\ volts\]
B.                    \[300\mu C;\ 75\ volts\]
C.                    \[800\mu C;\ 200\ volts\]
D.                    \[580\mu C;\ 145\ volts\]
Answer» E.
Discussion
6339.

Four plates of the same area of cross-section are joined as shown in the figure. The distance between each plate is\[d\]. The equivalent capacity across A and B will be

A.            \[\frac{2{{\varepsilon }_{0}}A}{d}\]
B.                    \[\frac{3{{\varepsilon }_{0}}A}{d}\]
C.                    \[\frac{3{{\varepsilon }_{0}}A}{2d}\]
D.                    \[\frac{{{\varepsilon }_{0}}A}{d}\]
Answer» C.                    \[\frac{3{{\varepsilon }_{0}}A}{2d}\]
Discussion
6340.

Three equal capacitors, each with capacitance \[C\] are connected as shown in figure. Then the equivalent capacitance between \[A\] and \[B\] is         [MP PET 1985, 89]

A.            \[C\]
B.                    \[3C\]
C.                    \[\frac{C}{3}\]
D.                    \[\frac{3C}{2}\]
Answer» C.                    \[\frac{C}{3}\]
Discussion
6341.

The capacities and connection of five capacitors are shown in the adjoining figure. The potential difference between the points \[A\] and \[B\] is \[60\ volts\]. Then the equivalent capacity between \[A\] and \[B\] and the charge on \[5\mu F\] capacitance will be respectively

A.            \[44\mu F;\ 300\mu C\]
B.                    \[16\mu F;\ 150\mu C\]
C.                    \[15\mu F;\ 200\mu C\]
D.                    \[4\mu F;\ 50\mu C\]
Answer» E.
Discussion
6342.

Four condensers are joined as shown in the adjoining figure. The capacity of each is\[8\mu F\]. The equivalent capacity between the points \[A\]and \[B\] will be

A.                    \[32\mu F\]
B.                    \[2\mu F\]
C.                    \[8\mu F\]
D.                    \[16\mu F\]
Answer» B.                    \[2\mu F\]
Discussion
6343.

Two condensers of capacities \[1\mu F\] and\[2\mu F\] are connected in series and the system is charged to\[120\ volts\]. Then the P.D. on \[1\mu F\] capacitor (in volts) will be    [MP PMT 1987]

A.                    40                                      
B.            60
C.                    80
D.            120
Answer» D.            120
Discussion
6344.

Three condensers each of capacitance \[2F\] are put in series. The resultant capacitance is                                                 [CPMT 1976; NCERT 1981; MP PMT 2001]

A.                    \[6F\]
B.                                      \[\frac{3}{2}F\]
C.                    \[\frac{2}{3}F\]
D.            \[5F\]
Answer» D.            \[5F\]
Discussion
6345.

A parallel plate capacitor is made by stacking \[n\] equally spaced plates connected alternately. If the capacitance between any two plates is \[C\] then the resultant capacitance is [NCERT 1971; DPMT 2001; MP PMT 2003; AIEEE 2005]

A.                    \[C\]
B.                                      \[nC\]
C.                    \[(n-1)C\]                      
D.            \[(n+1)C\]
Answer» D.            \[(n+1)C\]
Discussion
6346.

A parallel plate condenser is filled with two dielectrics as shown. Area of each plate is \[A\ metr{{e}^{2}}\]and the separation is\[t\ metre\]. The dielectric constants are \[{{k}_{1}}\] and \[{{k}_{2}}\] respectively. Its capacitance in farad will be                                                          [MNR 1985; DCE 1999; AIIMS 2001]

A.            \[\frac{{{\varepsilon }_{0}}A}{t}({{k}_{1}}+{{k}_{2}})\]
B.                    \[\frac{{{\varepsilon }_{0}}A}{t}.\frac{{{k}_{1}}+{{k}_{2}}}{2}\]
C.                    \[\frac{2{{\varepsilon }_{0}}A}{t}({{k}_{1}}+{{k}_{2}})\]
D.                    \[\frac{{{\varepsilon }_{0}}A}{t}.\frac{{{k}_{1}}-{{k}_{2}}}{2}\]
Answer» C.                    \[\frac{2{{\varepsilon }_{0}}A}{t}({{k}_{1}}+{{k}_{2}})\]
Discussion
6347.

The capacities of two conductors are \[{{C}_{1}}\]and \[{{C}_{2}}\] and their respective potentials are \[{{V}_{1}}\]and\[{{V}_{2}}\]. If they are connected by a thin wire, then the loss of energy will be given by [MP PMT 1986]

A.                    \[\frac{{{C}_{1}}{{C}_{2}}({{V}_{1}}+{{V}_{2}})}{2({{C}_{1}}+{{C}_{2}})}\]
B.                                      \[\frac{{{C}_{1}}{{C}_{2}}({{V}_{1}}-{{V}_{2}})}{2({{C}_{1}}+{{C}_{2}})}\]
C.                    \[\frac{{{C}_{1}}{{C}_{2}}{{({{V}_{1}}-{{V}_{2}})}^{2}}}{2({{C}_{1}}+{{C}_{2}})}\]             
D.            \[\frac{({{C}_{1}}+{{C}_{2}})({{V}_{1}}-{{V}_{2}})}{{{C}_{1}}{{C}_{2}}}\]
Answer» D.            \[\frac{({{C}_{1}}+{{C}_{2}})({{V}_{1}}-{{V}_{2}})}{{{C}_{1}}{{C}_{2}}}\]
Discussion
6348.

A capacitor of capacity \[{{C}_{1}}\]is charged to the potential of \[{{V}_{o}}\]. On disconnecting with the battery, it is connected with a capacitor of capacity \[{{C}_{2}}\] as shown in the adjoining figure. The ratio of energies before and after the connection of switch \[S\] will be

A.            \[({{C}_{1}}+{{C}_{2}})/{{C}_{1}}\]
B.                    \[{{C}_{1}}/({{C}_{1}}+{{C}_{2}})\]
C.                    \[{{C}_{1}}{{C}_{2}}\]
D.                    \[{{C}_{1}}/{{C}_{2}}\]
Answer» B.                    \[{{C}_{1}}/({{C}_{1}}+{{C}_{2}})\]
Discussion
6349.

Four capacitors of each of capacity \[3\mu F\]are connected as shown in the adjoining figure. The ratio of equivalent capacitance between \[A\] and \[B\] and between \[A\] and \[C\] will be

A.            4 : 3
B.                    3 : 4
C.                    2 : 3
D.                    3 : 2
Answer» B.                    3 : 4
Discussion
6350.

If three capacitors each of capacity \[1\mu F\]are connected in such a way that the resultant capacity is\[1.5\mu F\],  then [MP PET 1989]

A.                    All the three are connected in series
B.                    All the three are connected in parallel
C.                    Two of them are in parallel and connected in series to the third
D.            Two of them are in series and then connected in parallel to the third
Answer» E.
Discussion