In the adjoining figure, capacitor $(1)$ and $(2)$ have a capacitance $‘C’$ each. When the dielectric of dielectric consatnt $K$ is inserted between the plates of one of the capacitor, the total charge flowing through battery is
Advanced
Download our app for free and get started
Before insert dielectric, the equivalent capacitance $C_{e q}=\frac{C \times C}{C+C}=C / 2$
$Q_{e q}=C_{e q} E=C E / 2$
As battery is connected to capacitor so $E$ remains constant.
After insert dielectric $, C_{e q}^{\prime}=\frac{K C C}{K C+C}=\frac{K}{K+1} C$
$Q_{e q}^{\prime}=C_{e q}^{\prime} E=\frac{K}{K+1} C E$
Charge flow through the battery is $\Delta Q=Q_{e q}^{\prime}-Q_{e q}=\frac{K}{K+1} C E-\frac{C E}{2}=\frac{(K-1) C E}{2(K+1)}$
As $\mathrm{E}$ is constant so for inserting dielectric the charge on the capacitor will increase and it will flow from capacitance to battery to maintain constant $E$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1Two metal spheres of radii ${R_1}$ and ${R_2}$ are charged to the same potential. The ratio of charges on the spheres isView Solution
- 2Two thin wire rings each having a radius $R$ are placed at a distance $d$ apart with their axes coinciding. The charges on the two rings are $ + q$ and $ - q$. The potential difference between the centres of the two rings isView Solution
- 3In the following diagram the work done in moving a point charge from point $P$ to point $A$, $B$ and $C$ is respectively as $W_A$, $W_B$ and $W_C$ , thenView Solution
- 4Five identical plates each of area $A$ are joined as shown in the figure. The distance between the plates is $d$. The plates are connected to a potential difference of $V\;volts$. The charge on plates $1$ and $4$ will beView Solution
- 5View SolutionSome charge is being given to a conductor. Then its potential is
- 6View SolutionThe equivalent capacitance of the combination shown is
- 7The capacity of a condenser in which a dielectric of dielectric constant $5$ has been used, is $C$. If the dielectric is replaced by another with dielectric constant $20$, the capacity will becomeView Solution
- 8A thin conducting spherical shell (center at $O$ ) having charge $Q_0$ , radius $R$ and three point charges $Q_0$ , $-2Q_0$ , $3Q_0$ are also kept at point $A$ , $B$ and $C$ respectively as shown. Find the potential at any point on the conducting shell. (Potential at infinity is assumed to be zero)View Solution
- 9A potential difference of $300\, volts$ is applied to a combination of $2.0\,\mu F$ and $8.0\,\mu F$ capacitors connected in series. The charge on the $2.0\,\mu F$ capacitor isView Solution
- 10View SolutionThe potential gradient is a