The effective capacitance of combination of combination of equal capacitors between points A and B shown in figure is

C
2C
3C
^C⁄₂

Solution

A parallel plate capacitor is connected to a battery.The quantities charge, voltage,electric field and energy associated with this capacitor are given by Q₀, V₀, E₀, and U₀ respectively. A dielectric slab is now introduced to fill the space between the plates with the battery still in connection.The corresponding quantities now given by Q, V,E and U are related to the previous ones as

Q > Q₀
V > V₀
E> E₀
U < U₀

Solution

Two parallel plate capacitors of capacitances C and 2C are connected in parallel and charged to a potential difference V.The battery is then disconnected and the region between the plates of the capacitor C is completely filled with a material fo dielectric constant K.The potential difference across the capacitors now becomes

\(\frac{3V}{K+2}\)
KV
^V⁄_K
³⁄_KV

Solution

Two vertical metallic plates carrying equal and opposite charges are kept parallel to each other like a parallel plate capacitor. A small spherical metallic ball is suspended by along insulated thread such that it hangs freely in the centre of the two metallic plates. The ball, which is uncharged, is taken slowly towards the positively charged plate and is made to touch that plate. Then the ball will

stick to the positively charged plate
come back to its original position and will remain there
oscillate between the two plates touching each plate in turn
oscillate between the two plates without touch them

Solution

The ball on touching plate A will get positively charged. It will be repelled by A and get attracted towards B. After touching B it will get negatively charged.It will now be repelled by B and get attracted towards A.AB Thus it will remain oscillating and at the extreme position touch the plates.

Figure (i) shows two capacitors connected in series and connected by a battery. The graph (ii) shows the variation of potential as one moves from left to right on the branch AB containing the capacitors. Then

C₁ = C₂
C₁ < C₂
C₁ > C₂
C₁ and C₂ cannot be compared

Solution

Since, potential difference across C₂ is greater than C₁.

⇒ C₁ > C₂ [∵ v = ^q⁄_C and q is same in
series]

Three capacitors C₁, C₂ and C₃ are connected to a battery as shown. With symbols having their usual meanings, the correct conditions are

Q₁ = Q₂ = Q₃ and V₁ = V₂ = V
V₁ = V₂ = V₃ = V
Q₁ = Q₂ + Q₃ and V = V₁ = V₂
Q₂ = Q₃ and V₂ = V₃

Solution

C₂ and C₃ are parallel so V₂ = V₃

C₁ and combination of C₂ & C₃ is in series.

So, V = V₂ + V₁ or V = V₃ + V₁ and also Q₁ = Q₂ + Q₃

Between the plates of a parallel plate capacitor dielectric plate is introduced just to fill the space between the plates.The capacitor is charged and later disconnected from the battery. The dielectric plate is slowly drawn out of the capacitor parallel to plates. The plot of the potential difference V across the plates and the length of the dielectric plate drawn out is

Solution

Two small conductors A and B are given charges q₁ and q₂ respectively. Now they are placed inside a hollow metallic conductor C carrying a charge Q. If all the three conductors A,B and C are connected by a conducting wire as shown, the charges on A, Band C will be respectively

\(\frac{q_{1}+q_{2}}{2},\frac{q_{1}+q_{2}}{2},Q\)
\(\frac{Q+q_{1}+q_{3}}{3},\frac{Q+q_{1}+q_{2}}{3},\frac{Q+q_{1}+q_{2}}{3}\)
\(\frac{Q+q_{1}+q_{3}}{3},\frac{Q+q_{1}+q_{2}}{3},\frac{Q+q_{1}+q_{2}}{3}\)
0, 0, Q+ q₁ + q₂

Solution

Charge given to a hollow conductor resides only on the outer surface.

A parallel plate capacitor is located horizontally such that one of the plates is submerged in a liquid while the other is above the liquid surface. When plates are charged the level of liquid

rises
falls
remains unchanged
may rise or fall depending on the amount of charge

Solution

The molecules of liquid will convert into induced dipole, get oriented along the electric field produced between the plates and rise due to force of attraction.

In the circuit shown, which of the following statements is true if V₁(potential across C₁) is 30 V and V₂(potential across C₂) is 20 V?

With S₁ closed, V₁ = 15 V, V₂= 25 V
With S₃ closed, V₁ = V₂= 25 V
With S₁ and S₂ closed, V₁ = V₂ = 0
With S₁ and Ssub>3 closed, V₁ = 30 V,V₂= 20 V

Solution

When S₁ and S₃ is closed V₁= 30 V and potential drop across C₂ becomes 20 V.

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