Two identical capacitors are connected parallel. Initially they are charged to a potential V₀ and each acquired a charge Q₀. The battery is then disconnected, and the gap between the plates of one capacitor is filled with a dielectric κ.(a) What is the new potential difference V across the capacitors. possible asnwers: V=(V₀)^2/[kQ₀+V₀), V=V₀/2k, V=V₀/2, V=kQ₀/V₀, V=2V₀/[k+1](b) If the dielectric constant is 7.8, calculate the ratio of the charge on the capacitor with the dielectric after it is inserted as compared with the initial charge.

ΔV ’= 2Δv / (1 + k) ,            Q’= Q₀ 1,772

Explanation:

When the capacitors are connected in series the capacitance is added

      C_eq = C₁ + C₂2

     C_eq = 2 C₀

     ΔV = Q₀ / C_eq

     ΔV = Q₀ / 2 C₀

In this case, a dielectric is introduced to one of the capacitors, so its capacity changes.

         C₂’= k C₂

Since the two capacitors have the same initial value let's call Co

          C_eq’= C₀ (1 + k)

The set charge is

           C_eq ’= Q₀ / ΔV’

            ΔV ’= Q₀ / Ceq’

            ΔV ’= Q₀ / C₀ (1 + k)

The relationship between these voltages is

            ΔV'/ ΔV = 2 / (1 + k)

            ΔV ’= 2Δv / (1 + k)

The initial charge of the capacitor is

              Q₀ = C₀ ΔV

The charge after introducing the dielectric is

             Q’= k C₀ ΔV’

             Q ’= k C₀ 2 ΔV / (1 + k)

             Q’= Q₀ 2k / (1 + k)

             Q’= Q₀  2 7.8 /(1+7.8)

              Q’= Q₀ 1,772

sonar - device which is used to find the submit submarines, sankalp ship. sonar waves consists of a transmitter and detector which are installed in the observation centre on board of a ship. the ultrasonic waves are sent into the sea at high frequency about 1000 khz in all direction.

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.