Three uncharged capacitors of capacitance C1,C2 and C3 are connected as shown in figure to one another 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 figure to one another 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-r6fscsvtzaetvexs.jpg" /> (A) (VA C1 + VB C2 + VD C3/C1 + C2 + C3) (B) (VA VB VD/C1 C2 + C2 C3 + C3 C1) (C) (VA + VB + VD/C1 + C2 + C3) (D) (VA VB + VB VD + VD VA/C1 + C2 + C3)

Tardigrade Admin · Accepted Answer

VA-V0=(q/C1) or q=(VA - V0)C1 VB-V0=(q1/C2) or q1=(VB - V0)C2 VD-V0=(q2/C3) or q2=(VD - V0)C3 q+q1+q2=0 ( VA - V0)C1+(VB - V0)C2+(VD - V0)C3=0 ∴ V0=(VA C1 + VB C2 + VD C3/C1 + C2 + C3)

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

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

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

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

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

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

C1​+C2​+C3​VA​C1​+VB​C2​+VD​C3​​

C1​C2​+C2​C3​+C3​C1​VA​VB​VD​​

C1​+C2​+C3​VA​+VB​+VD​​

C1​+C2​+C3​VA​VB​+VB​VD​+VD​VA​​

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

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

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

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

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