Three capacitors ${C}_{1}=2\, \mu {F}, {C}_{2}=6 \, \mu {F}$ and ${C}_{3}=12 \, \mu {F}$ are connected as shown in figure. Find the ratio of the charges on capacitors ${C}_{1}, {C}_{2}$ and ${C}_{3}$ respectively:
JEE MAIN 2021, Diffcult
Download our app for free and get started
$\left(V_{D}-V\right) C_{2}+\left(V_{D}-0\right) C_{3}=0$
$\left(V_{D}-V\right) 6+\left(V_{D}-0\right) 12=0$
$V_{D}-V+2 V_{D}=0$
$V_{D}=\frac{V}{3}$
${q}_{2}=\left({V}-{V}_{{D}}\right) {C}_{2}=\left({V}-\frac{{V}}{3}\right)(6 \mu {F})$
${q}_{2}=(4 {V}) \mu {F}$
${q}_{3}=\left({V}_{{D}}-0\right) {C}_{3}=\frac{{V}}{3} \times 12 \mu {F}=4 {V} \mu {F}$
${q}_{1}=({V}-0) {C}_{1}={V}(2 \mu {F})$
${q}_{1}: {q}_{2}: {q}_{3}=2: 4: 4$
${q}_{1}: {q}_{2}: {q}_{3}=1: 2: 2$
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
- 1A series combination of three capacitors of capacities $1\,\mu \,F,\,2\,\mu \,F$ and $8\,\mu \,F$ is connected to a battery of $e.m.f.$ $13\, volt$. The potential difference across the plates of $2\,\mu \,F$ capacitor will be.....$V$View Solution
- 2From a supply of identical capacitors rated $8\ \mu F$, $250\ V$, the minimum number of capacitors required to form a composite $16$ $\mu F$, $1000$ $V$ is :View Solution
- 3In the circuit shown, $q_2$ and $q_3$ are respectively (Initially all capacitors are uncharged)View Solution
- 4A network of four capacitors of capacity equal to $C_1 = C, C_2 = 2C, C_3 = 3C$ and $C_4 = 4C$ are conducted in a battery as shown in the figure. The ratio of the charges on $C_2$ and $C_4$ isView Solution
- 5Electric field at a place is $\overrightarrow {E\,} = {E_0}\hat i\,V/m$ . A particle of charge $+q_0$ moves from point $A$ to $B$ along a circular path find work done in this motion by electric fieldView Solution
- 6Three capacitors of $2.0,\;3.0$ and $6.0\;\mu F$ are connected in series to a $10\,V$ source. The charge on the $3.0\,\mu F$ capacitor is........$\mu C$View Solution
- 7In 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 $W_C$, then (there is no charge nearby)View Solution
- 8In the given circuit, the charge on $4\, \mu F$ capacitor will be.....$\mu C$View Solution
- 9The distance between the plates of a parallel plate condenser is $\,4mm$ and potential difference is $60\;volts$. If the distance between the plates is increased to $12\,mm$, thenView Solution
- 10View SolutionIf a unit positive charge is taken from one point to another over an equipotential surface, then