The equivalent capacitance of three capacitors of capacitance ${C_1},{C_2}$ and ${C_3}$ are connected in parallel is $12$ units and product ${C_1}.{C_2}.{C_3} = 48$. When the capacitors ${C_1}$ and ${C_2}$ are connected in parallel, the equivalent capacitance is $6$ units. Then the capacitance are
A$2, 3, 7$
B$1.5, 2.5, 8$
C$1, 5, 6$
D$4, 2, 6$
Medium
Download our app for free and get started
D$4, 2, 6$
d (d) ${C_1}+{C_2}+{C_3} = 12$....$(i)$
${C_1}.{C_2}.{C_3} = 48$....$(ii)$
$C_1 + C_2 = 6$ ....$(iii)$
From equation $(i)$ and $(iii)$
$C_3 = 6$ ....$(iv)$
From equation $(ii)$ and $(iv)$ $C_1C_2 = 8$
Also ${({C_1} - {C_2})^2} = {({C_1} + {C_2})^2} - 4{C_1}{C_2}$
${({C_1} - {C_2})^2} = {(6)^2} - 4 \times 8 = 4$
$==>$ $ C_1 -C_2 = 2$.....$(v)$
On solving $(iii)$ and $(v)$ $C_1 = 4,\,\, C_2 = 2 $
Download our app
and 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.*
A charge $3$ coulomb experiences a force $3000$ $N$ when placed in a uniform electric field. The potential difference between two points separated by a distance of $1$ $cm$ along the field lines is.....$V$
The distance between charges $+\mathrm{q}$ and $-\mathrm{q}$ is $2 l$ and between $+2 \mathrm{q}$ and $-2 \mathrm{q}$ is $4 l$. The electrostatic potential at point $P$ at a distance $r$ from centre $O$ is $-\alpha\left[\frac{q l}{r^2}\right] \times 10^9 \mathrm{~V}$, where the value of $\alpha$ is____. (Use $\left.\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{Nm}^2 \mathrm{C}^{-2}\right)$
A metallic spherical shell has an inner radius $R_1$ and outer radius $R_2$. A charge $Q$ is placed at the centre of the spherical cavity. What will be surface charge density on the inner surface
The switch $S$ shown in figure is kept closed for a long time and then opened at $t = 0$, then the current in the middle $20\, \Omega$ resistor at $t = 0.25\, ms$ is :-
Within a spherical charge distribution of charge density $\rho \left( r \right)$, $N$ equipotential surfaces of potential ${V_0},{V_0} + \Delta V,{V_0} + 2\Delta V,$$.....{V_0} + N\Delta V\left( {\Delta V > 0} \right),$ are drawn and have increasing radii $r_0, r_1, r_2,......r_N$, respectively. If the difference in the radii of the surfaces is constant for all values of $V_0$ and $\Delta V$ then
A capacitor $C_1$ is charged up to a voltage $V\, = 60\,V$ by connecting it to battery $B$ through switch $( 1)$, Now $C_1$ is disconnected from battery and connected to a circuit consisting of two uncharged capacitors $C_2\, = 3.0\,\mu F$ and $C_3\,= 6.0\,\mu F$ through a switch $(2)$ as shown in the figure. The sum of final charges on $C_2$ and $C_3$ is......$\mu C$
A charge of total amount $Q$ is distributed over two concentric hollow spheres of radii $r$ and $R ( R > r)$ such that the surface charge densities on the two spheres are equal. The electric potential at the common centre is
Two concentric hollow metallic spheres of radii $r_1$ and $r_2 (r_1 > r_2)$ contain charges $q_1$ and $q_2$ respectively. The potential at a distance $x$ between $r_1$ and $r_2$ will be