Two condensers, one of capacity $C$ and other of capacity $C/2$ are connected to a $V-$ volt battery, as shown in the figure. The work done in charging fully both the condensers is
AIPMT 2007, Medium
Download our app for free and get started
As the capacitors are connected in parallel, therefore potential difference across both the condensors remains the same.
$\therefore Q_{1}=C V ;$
$Q_{2} =\frac{C}{2} V $
$\text { Also }, Q =Q_{1}+Q_{2}$
$ = CV+\frac{C}{2} V=\frac{3}{2} C V$
Work done in charging fully both the condensors is given by
$W=\frac{1}{2} Q V=\frac{1}{2} \times\left(\frac{3}{2}\, C V\right) V=\frac{3}{4} \,C V^{2}$
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
- 1The plates of a parallel plate capacitor with no dielectric are connected to a voltage source. Now a dielectric of dielectric constant $K $ is inserted to fill the whole space between the plates with voltage source remaining connected to the capacitor.View Solution
- 2A parallel plate capacitor with air between the plates has capacitance of $9\ pF$. The separation between its plates is '$d$'. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant $k_1 = 3$ and thickness $\frac{d}{3}$ while the other one has dielectric constant $k_2 = 6$ and thickness $\frac{2d}{3}$ . Capacitance of the capacitor is now.......$pF$View Solution
- 3View SolutionConsidering a group of positive charges, which of the following statements is correct?
- 4Two condensers ${C_1}$and ${C_2}$ in a circuit are joined as shown in figure. The potential of point $A$ is ${V_1}$ and that of $B$ is ${V_2}$. The potential of point $D$ will beView Solution
- 5A $60\; pF$ capacitor is fully charged by a $20\; \mathrm{V}$ supply. It is then disconnected from the supply and is connected to another uncharged $60 \;pF$ capactior is parallel. The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in $nJ$)View Solution
- 6In the following diagram, the charge and potential difference across $8\, \mu F$ capacitance will be nearlyView Solution
- 7Four metal conductors having different shapesView Solution
$1.$ A sphere $2.$ Cylindrical
$3.$ Pear $4.$ Lightning conductor
are mounted on insulating stands and charged. The one which is best suited to retain the charges for a longer time is
- 8If charge on each plate of a parallel plate capacitor is $Q$ and the magnitude of electric field between the plates is $E$ then force on each plate of a parallel plate capacitor will beView Solution
- 9For given $\vec E = 2x\hat i + 3y\hat j$, find the potential at $(X, Y)$ if potential at origin is $5\, volts.$View Solution
- 10Two identical parallel plate capacitors of capacitance $C$ each are connected in series with a battery of emf, $E$ as shown below. If one of the capacitors is now filled with a dielectric of dielectric constant $k$, then the amount of charge which will flow through the battery is (neglect internal resistance of the battery)View Solution
