Three uncharged capacitors of capacitance C1,C2 and C3 are connected as shown in the figure to one another at point O and to points A,B and D at potentials VA, VB and VD. Then the potential at O will be,:

Question

Three uncharged capacitors of capacitance C1,C2 and C3 are connected as shown in the figure to one another at point O and to points A,B and D at potentials VA, VB and VD. Then the potential at O will be,: <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-a9zqvdoq342xxdsx.jpg" /> (A) (VA + VB + VD/C1 + C2 + C3) (B) (VA C1 + VB C2 + VD C3/C1 + C2 + C3) (C) (VA VB + VB VD + VD VA/C1 + C2 + C3) (D) (VA VB VD/C1 C2 + C2 C3 + C3 C1)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-a9zqvdoq342x0zkl.jpg" /> VA-V=(q1/C1) VB-V=(q2/C2) VD-V=(q3/C3) q1+q2+q3=0 (C1 VA + C2 VB + VD C3/C1 + C2 + C3)=V

Q. Three uncharged capacitors of capacitance $C_{1}, C_{2}$ and $C_{3}$ are connected as shown in the figure to one another at point $O$ and to points $A, B$ and $D$ at potentials $V_{A},$ $V_{B}$ and $V_{D} .$ Then the potential at $O$ will be, :

$\frac{V _{A} + V _{B} + V _{D}}{C _{1} + C _{2} + C _{3}}$

$\frac{V _{A} C _{1} + V _{B} C _{2} + V _{D} C _{3}}{C _{1} + C _{2} + C _{3}}$

$\frac{V _{A} V _{B} + V _{B} V _{D} + V _{D} V _{A}}{C _{1} + C _{2} + C _{3}}$

$\frac{V _{A} V _{B} V _{D}}{C _{1} C _{2} + C _{2} C _{3} + C _{3} C _{1}}$

$V_{A} - V = \frac{q _{1}}{C _{1}}$
$V_{B} - V = \frac{q _{2}}{C _{2}}$
$V_{D} - V = \frac{q _{3}}{C _{3}}$
$q_{1} + q_{2} + q_{3} = 0$
$\frac{C _{1} V _{A} + C _{2} V _{B} + V _{D} C _{3}}{C _{1} + C _{2} + C _{3}} = V$

Q. Three uncharged capacitors of capacitance C1​,C2​ and C3​ are connected as shown in the figure to one another at point O and to points A,B and D at potentials VA​, VB​ and VD​. Then the potential at O will be, :

C1​+C2​+C3​VA​+VB​+VD​​

C1​+C2​+C3​VA​C1​+VB​C2​+VD​C3​​

C1​+C2​+C3​VA​VB​+VB​VD​+VD​VA​​

C1​C2​+C2​C3​+C3​C1​VA​VB​VD​​