A network of four capacitors of capacity equal to C₁ = C,C₂= 2C, C₃= 3C and C₄= 4C are conducted to a battery as shown in the figure. The ratio of the charges on C₂ and C₄ is

4/7
3/22
7/4
22/3

Solution

Two charges q₁ and q₂ are placed 30 cm apart, as shown in the figure. A third charge q3 is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is \(\frac{_{3}}{4\pi \epsilon _{0}}K\), where k is

8q₁
6q₁
8q₂
6q₂

Solution

As per this diagram a point charge +q is placed at the origin O. Work done in taking another point charge – Q from the point A [coordinates (0, a)] to another point B[coordinates (a, 0)] along the straight path AB is

zero
\(\left ( \frac{-qQ}{4\pi \varepsilon _{0}a^{2}}\frac{1}{a^{2}} \right )\sqrt{2}a\)
\(\left ( \frac{qQ}{4\pi \varepsilon _{0}a^{2}}\frac{1}{a^{2}} \right )\frac{a}{\sqrt{2}}\)
\(\left ( \frac{qQ}{4\pi \varepsilon _{0}a^{2}}\frac{1}{a^{2}} \right )\sqrt{2}a\)

Solution

A capacitor C₁ is charged to a potential difference V.The charging battery is then removed and the capacitor is connected to an uncharged capacitor C₂. The potential difference across the combination is

\(\frac{VC_{1}}{(C_{1}+C_{2})}\)
\(\left ( V_{1}+\frac{C_{2}}{C_{1}} \right )\)
\(\left ( V_{1}+\frac{C_{1}}{C_{2}} \right )\)
\(\frac{VC_{2}}{(C_{1}+C_{2})}\)

Solution

In a parallel plate capacitor, the distance between the plates is d and potential difference across plates is V. Energy stored per unit volume between the plates of capacitor is

\(\frac{Q^{2}}{2V^{2}}\)
\(\frac{1}{2}\varepsilon _{0}\frac{V^{2}}{d^{2}}\)
\(\frac{1}{2}\frac{V^{2}}{\varepsilon _{0}d^{2}}\)
\(\frac{1}{2}\varepsilon _{0}\frac{V^{2}}{d^{2}}\)

Solution

What is the effective capacitance between points X and Y?

24 μF
18 μF
12 μF
6 μF

Solution

A parallel plate condenser with oil between the plates(dielectric constant of oil K = 2) has a capacitance C. If the oil is removed, then capacitance of the capacitor becomes

√2C
2 C
^C⁄_√2
^C⁄₂

Solution

A 4μF capacitor, a resistance of 2.5 MΩ is in series with 12V battery. Find the time after which the potential difference across the capacitor is 3 times the potential diference across there sistor. [Given In(b) = 0.693]

13.86s
6.93 s
7s
14 s

Solution

In the given circuit if point C is connected to the earth and a potential of +2000 V is given to the point A, the potential at B is

1500 V
1000 V
500 V
400 V

Solution

A dielectric slab of thickness dis inserted in a parallel plate capacitor whose negative plate is at x= 0 and positive plate is at x= 3d. The slab is equidistant from the plates. the capacitor is given some charge. As one goes from 0 to 3d

the magnitude of the electric field remains the same
the direction of the electric field remains the same
the electric potential decreases continuously
the electric potential increases at first, then decreases and again increases

Solution

Even after introduction of dielectric slab,direction of electric field will be perpendicular to the plates and directed from positive plate to negative plate.

Further, magnitude of electric field in air = \(\frac{\sigma }{\varepsilon _{0}}\)

Magnitude of electric field in dielectric = \(\frac{\sigma }{K\varepsilon _{0}}\)

Similarly electric lines always flows from higher to lower potential, therefore, electric potential in ceases continuously as we move from x = 0 to x = 3d.

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