Question

Dielectrics play an important role in design of capacitors. The molecules of a dielectric may be polar or non-polar. When a dielectric slab is placed in an external electric field, opposite charges appear on the two surfaces of the slab perpendicular to electric field. Due to this an electric field is established inside the dielectric. The capacitance of a capacitor is determined by the dielectric constant of the material that fills the space between the plates. Consequently, the energy storage capacity of a capacitor is also affected. Like resistors, capacitors can also be arranged in series and/or parallel.

Two capacitors of capacitances 2 C₀ and 6 C₀ are first connected in series and then in parallel across the same battery. The ratio of energies stored in series combination to that in parallel is ______.

Options

• `1/4`

• `1/6`

• `2/15`

• `3/16`

Answer 1

Two capacitors of capacitances 2 C₀ and 6 C₀ are first connected in series and then in parallel across the same battery. The ratio of energies stored in series combination to that in parallel is `bbunderline(3/16)`.

Explanation:

For series combination,

`1/C_s = 1/(2C_0) + 1/(6C_0)`

`1/C_s = (3 + 1)/(6C_0)`

⇒ `C_s = (3C_0)/2`

Energy stored, `u_s = 1/2C_sV^2`

`u_s = 1/2((3C_0)/2)V^2`

For parallel combination,

C_p = 2C₀ + 6C₀

C_p = 8C₀

Energy stored, `u_p = 1/2C_pV^2`

`u_p = 1/2(8C_0)V^2`

Now, `u_s/u_p = (3/2C_0)/(8C_0)`

`u_s/u_p = 3/16`