In a Van-de-Graff type generator, a spherical metal shell is to be a 15×${10}^6$ V electrode. The dielectric strength of the gas surrounding the electrode is $5\times {10}^7$ V/m. What is the minimum radius of the spherical shell required?

1. 20 cm
2. 30 cm
3. 25 cm
4. 35 cm

A parallel plate capacitor is to be designed with a voltage rating of 1 kV, using a material of dielectric constant 3 and dielectric strength of about 10⁷ V m^-1. For safety, we should like the field never to exceed, say 10% of the dielectric strength. What minimum area of the plates is required to have a capacitance of 50 pF?
 
1. 19 cm²
2. 17 cm²
3. 15 cm²
4. 23 cm²

A cylindrical capacitor has two co-axial cylinders of length \(15~\text{cm}\) and radii \(1.5~\text{cm}\) and \(1.4~\text{cm}\). The outer cylinder is earthed and the inner cylinder is given a charge of \(3.5~\mu \text{C}\).  The capacitance of the system is:
1. \(3.4 \times10^{-10}~\text{F}\) 
2. \(1.2 \times10^{-10}~\text{F}\)
3. \(4.8 \times10^{-9}~\text{F}\)  
4. \(2.5 \times10^{-9}~\text{F}\)  

A spherical capacitor has an inner sphere of radius \(12\) cm and an outer sphere of radius \(13\) cm. The outer sphere is earthed and the inner sphere is given a charge of \(2.5\) $\mu$C. The space between the concentric spheres is filled with a liquid of dielectric constant \(32.\) The capacitance of the capacitor is:
1. \(4.0\times 10^{-9}\) F
2. \(4.5\times 10^{-9}\) F
3. \(5.5\times 10^{-9}\) F
4. \(3.3\times 10^{-9}\) F

If \(Q\) is the charge on the capacitor, and \(E\) is the magnitude of the electric field between the plates. Then force on each plate of a parallel plate capacitor has a magnitude equal to:
1. \(\dfrac{1}{2}QE\)
2. \(QE\)
3. \(2QE\)
4. \(0\)

A 4 $\mu$F capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 2 $\mu$F capacitor. How much electrostatic energy of the first capacitor is lost in the form of heat and electromagnetic radiation?

1. 3.10×10^-2J
2. 3.33×10^-3 J
3.1.23×10^-2 J
4.2.67×10^-2 J

The plates of a parallel plate capacitor have an area of \(90\) cm² each and are separated by \(2.5\) mm. The capacitor is charged by connecting it to a \(400\) V supply. How much electrostatic energy is stored by the capacitor?
1. \(1.7\times10^{-6}\) J
2. \(2.12\times10^{-6}\) J
3. \(2.55\times10^{-6}\) J
4. \(1.66\times10^{-6}\) J

The equivalent capacitance of the circuit is:

  
1. \(200\) pF
2. \(\frac{200}{3}\) pF
3. \(200\) \(\mu\)F
4. \(150\) pF$$
 

What is the area of the plates of a \(2~\text{F}\) parallel plate capacitor, given that the separation between the plates is \(0.5~\text{cm}\)?
1. \(1100~\text{km}^2\)
2. \(1130~\text{km}^2\)
3. \(1110~\text{km}^2\)
4. \(1105~\text{km}^2\)

Two charged conducting spheres of radii a and b are connected to each other by a wire.  The ratio of electric fields at the surfaces of the two spheres is:
1. \(\frac{a}{b}\)
2. \(1\)
3. \(\frac{2a}{b}\)
4. \(\frac{b}{a}\)