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101.

Area of each plate is `A`. The conducting plates are connected to a battery of emf `V` volts. Find charges `q_1` to `q_t`.

Answer» Net charge drawn from the battery is zero or
`q_(Total)=0`
`:. q_1=q_6=q_(Total)/2=0`
`V_(AB)=V` with `V_AgtV_B`
`:. |q_2|=|q_3|=CV=((epsilon_0A)/d)V`
`q_2=+(epsilon_0AV)/d and q_3=-(epsilon_0AV)/d`
similarly,
`V_(BC)=V with V_CgtV_B`
`:. |q_4|=|q_5|=CV=((epsilon_0A)/(2d))V`
with `q_5=(epsilon_0AV)/(2d)` and `q_4=-(epsilon_0AV)/(2d)`
Discussion
102.

A `muF` capacitor `C_1` is charged to `V_0 = 120 V`. The charging battery is then removed and the capacitor is connected in parallel to an uncharged `+ 4muF` capacitor `C_2`. (a) what is the potential difference `V` across the combination? (b) what is the stored energy before and after the switch `S` is closed?

Answer» Correct Answer - C::D
a. `V=q_(n et)/C_(n et)=(C_1V_0)/(C_1+C_2)=V_0/(1+C_2//C_1)`
`=120/(1+4//8)=80V`
b. `U_i=1/2C_1V_0^2=1/2xx8xx10^-6xx(120)^2`
`=5.76xx10^-2J`
`U_f=1/2(C_1+C_2)V^2`
`=1/2(C_1+C_2)V^2`
`=1/2xx12xx10^-6xx(80)^2`
`=3.81xx10^-2J`
Discussion
103.

A capacitor of capacitance `C_1 = 1.0muF` charged upto a voltage `V = 110 V` is connected in parallel to the terminals of a circuit consisting of two uncharged capacitors connected in series and possessing the capacitance `C_2 = 2.0 muF` and `C_3 = 3.0muF`. What charge will flow through the connecting wires?

Answer» Correct Answer - C
`C_23=(2xx3)/(2+3)=1.2muF`
` q_("total")=C_1V=110muC`
Common potential in parallel is given by
`V=("Total charge")/("Total capacity")`
`=110/(1+1.2)=50V`
`q_23=(C_23)V=60muC`
So, this much charge flows through the switch.
Discussion
104.

A parallel plate capacitor is charged and then the battery is disconnected. When the plates of the capacitor are brought closer, thenA. energy stored in the capacitor decreasesB. the potential differences between the plates decreasesC. the capacitance increasesD. the electric field between the plates decreases

Answer» Correct Answer - A::B::C
If the battery is disconected, then `q=`constant
`C=(epsilon_0A)/d or Cprop1/d`
d is decreased. Hence, C will increase.
`U=1/2q^2/c or U prop 1/C`
C is increasing.Hence U will decrease.
`V=q/C or Vprop1/C`
`C` is increasing. Hence, `V` will decrease.
Discussion
105.

A `10.0muF` parallel-plate capacitor with circular plates is connected to a `12.0 V` battery.(a) What is the charge on each plate?(b) How much charge would be on the plates if their separation were doubled while the capacitor remained connected to the battery? (c) How much charge would be on the plates if the capacitor were connected to the `12.0 V` batter `Y` after the radius of each plate was doubled without changing their separation?

Answer» Correct Answer - C::D
a. `q=CV`
b. `C=(epsilon_0A)/d` or `Cprop1/d`
if d is doubled, `C` will remain half. Hence `q` will also remain half.
`c.q=CV=((epsilon_0A)/d)V=(epsilon_0(piR^3)V)/d`
`orqpropR^2`
`R` is doubled. Hence q will become four times or `480 muC`
Discussion
106.

Calculate the capacitance of a sherial capacitor consisting of two concentric spherical conductros of radii a and b(bgta), when the outer one is charged and the inner is earthed. The space between the spheres is filled by insulating material of relative permittivity `epsilon_(r)`.

Answer» Correct Answer - `4piepsilon_(0)((epsilon_(r)-1)ab+b^(2))/(b-a)`
Discussion
107.

`N` drops of mercury of equal radii and possessing equal charges combine to from a big drop. Compare the charge, capacitance and potential of bigger drop with the corresponding quantities of individual drops.

Answer» Correct Answer - `N,N^(1//3),N^(2//3)`
Discussion
108.

Calculate the capacitance of the capacitor `C` in Fig. The equivalent capacitance of the combination between `P` and `Q` is `30 mu F`

Answer» Correct Answer - `60muF`
Discussion