# Capacitance IITJEE TEST Series

(A) Multiple choice questions with one or more then one correct answers

1. Which one of the following statement(s) is true
a. When the space between conductors of a capacitor is filled by dielectric it's capacitance decreases.
b. When the space between conductors of a capacitor is filled by dielectric it's capacitance increases.
c. When the space between conductors of a capacitor is filled by dielectric it's capacitance is increased by a factor known as dielectric constant of the dielectric
d. On introduction of dielectric between the conductors of capacitor , dielectric will reduce both electric field and potential difference

2 A parallel plate air capacitor is charged by cinnecting both of it's plates to the battery now a dielectric of dielectric constant k is inserted without disconnecting the battery which causes
a. Increase in potential difference across the plates and reduction in stored energy and no change in charge of plates.
b. The battery to supply the more charge to maintain the original potential difference and charge on plates increases.
c. Reduction of charge on the plates and increase of potential difference across the plates.
d None of the above.

3. For the arrangement shown below in the figure 1 total effective capacitance between the terminals is
a. 12.5 μF
b. 4.4 μF
c. 15.2 μF
d. 14 μF

4. The two plates of a capacitor are given charges ±Q and then they are immersed in a tank of oil . the electric field between the plates
a. increases
b. decreases
c. remain same
d. none of the above

ans b

5. The net capacitance of capacitors in figure 2 beetween points a and b is a. 1 μF
b. 3μF
c. 4 μF
d 2 μF

(A) A parallel plate capacitor of area A and separation d is charged to a potential difference V and is removed from the charging source. A dielectric slab of dielectri constant k=2 , thickness d and area A/2 is inserted between the plates of the capacitor as shown below in the fig. 1. Which one of the following statement(s) is correct
a. Electric field have different values inside the dielectric as in the free space between the plates.
b. Electric field have same values inside the dielectric as in the free space between the plates.
c. There will be diferent potential difference between the portion of the plate separated by dielectric slab an between the portion separated by the vacuum.
d. none of the above.

2. If τ1 be the surface charge density at the conductor-dielectric surface and τ2 be the charge density at the conductor vacuum-surfacethen ratio betwen the two charge densities is
a. τ12=2:1
b. τ12=1:2
c. τ12=2:2
d. τ12=4:1

3. If C is the capacitance of the capacitor without the dielectric slab and V is the potential diffrence then capacitance and potential diffrence of capacitor on introduction of dielectric is
a. 3C/2 ; 3V/2
b. 2C/3 ; 2V/3
c. 2C/3 ; 3V/2
d. 3C/2 ; 2V/3

(B) The space between the plates of a parallel plate capacitor is filled consicutively with two dielectric layers having thickness d1 and d2 and permitivities ε1 and ε2 respectively and area of each plate is A.

1. After the introduction of dielectric slabs the capacitance of the capacitor is
a. ε0A/[(d11)+(d21)]
b. ε0/A[(ε1/d1)+(ε2/d2)]
c. ε0d1d2/A(ε12)
d. ε0A/d1d212)

2. If the voltage across the capacitor is V and electric field is directed from layer 1 to layer 2 then density of boundary charge on boundary plane is
a. (ε2d11d2)/ε0V(ε12)
b. ε0V(ε12)/(ε2d11d2)
c. ε0V/(ε2d11d2)
d. ε0V(ε12)/(ε2d11d2)