Electrostatic Potential and Capacitance

A parallel plate capacitor is charged and then isolated. The effect of increasing the plate separation on charge, potential and capacitance respectively are

• constant, decreases, increases

• constant, decreases, decreases

• constant, increases, decreases

• increases, decreases, decreases

Three point charges 3 nC, 6 nC and 9 nC are placed at the corners of an equilateral triangle of side 0.1 m. The potential energy of the system is

• 991 μJ

• 8910 μJ

• 891 μJ

• 99100 μJ

Nature of equipotential surface for a point charge is

• Ellipsoid with charge at foci

• Sphere with charge at the centre of the sphere

• Sphere with charge on the surface of the sphere

• Plane with charge on the surface

A capacitor of 8 Fis connected as shown in the figure. Charge on the plates of the capacitor

• 32 C

• 40 C

• 0 C

• 80 C

Four metal plates are arranged as shown in the figure. Capacitance between X and Y (A ➔ Area of each plate, d ➔ distance between the plates) is

• $\frac{3}{2} \frac{{\mathrm{\epsilon }}_0\mathrm{A}}{\mathrm{d}}$

• $\frac{2{\mathrm{\epsilon }}_0\mathrm{A}}{\mathrm{d}}$

• $\frac{2}{3} \frac{{\mathrm{\epsilon }}_0\mathrm{A}}{\mathrm{d}}$

• $\frac{3{\mathrm{\epsilon }}_0\mathrm{A}}{\mathrm{d}}$

A capacitor of capacitance 10 µF is connected to an AC ammeter. If the source voltage varies as $\mathrm{V} = 50\sqrt{2} \sin 100 \mathrm{t}$, the reading of the ammeter is

• 50 mA

• 70.7 mA

• 5.0 mA

• 7.07 mA

The minimum value of effective capacitance that can be obtained by combining 3 capacitors of capacitances 1 pF, 2 pF and 4 pF

• $\frac{4}{7} \mathrm{pF}$

• 1 pF

• 2 pF

• $\frac{7}{4} \mathrm{pF}$

A system of two capacitors of capacitance 2 μFand 4 µF is connected in series across a potential difference of 6V. The electric charge and energy stored in a system are

• 36 μC and 108 μJ

• 8 μC and 24 μJ

• 1 μC and 3 μJ

• 10 μC and 30 μJ

Two capacitors of capacitances 3 µF and 6 µF are charged to a potential of 12 V each. They are now connected to each other, with the positive plate to each joined to the negative plate to the other. The potential difference across each will be

• 4V

• 6V

• zero

• 3V

What fraction of the energy drawn from the charging battery is stored in a capacitor ?

• 75 %

• 100 %

• 25 %

• 50 %