Three uncharged capacitors of capacities C1 , C2 and C3 are connected as shown in the figure. A, B and C are at potentials V1, V2 and V3 respectively. The potential at ‘O' is

Question

Three uncharged capacitors of capacities C1 , C2 and C3 are connected as shown in the figure. A, B and C are at potentials V1, V2 and V3 respectively. The potential at ‘O' is (A) (C1 V1+C2 V2+C3 V3/C1+C2+C3) (B) (C1 V1+C2 V2-C3 V3/C1+C2+C3) (C) (C1 V1-C2 V2-C3 V3/C1+C2+C3) (D) (C1 V1-C2 V2+C3 V3/C1+C2+C3)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/668523c1e2fc3e6b460cf1c5f884ddb8-.png" /> Total charge in the capacitors (accumulated at point O ) Q text total =C1 V1+C2 V2+C3 V3 Total capacitance of the combination, C text total =C1+C2+C3 (w.r.t. point . O) So, potential at O, V = (Q texttotal/C texttotal) =(C1 V1+C2 V2+C3 V3/C1+C2+C3)

Q. Three uncharged capacitors of capacities $C_{1}, C_{2}$ and $C_{3}$ are connected as shown in the figure. A, B and C are at potentials $V_{1}, V_{2}$ and $V_{3}$ respectively. The potential at ‘O' is

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

$\frac{C _{1} V _{1} + C _{2} V _{2} - C _{3} V _{3}}{C _{1} + C _{2} + C _{3}}$

$\frac{C _{1} V _{1} - C _{2} V _{2} - C _{3} V _{3}}{C _{1} + C _{2} + C _{3}}$

$\frac{C _{1} V _{1} - C _{2} V _{2} + C _{3} V _{3}}{C _{1} + C _{2} + C _{3}}$

Zero

Q. Three uncharged capacitors of capacities C1​,C2​ and C3​ are connected as shown in the figure. A, B and C are at potentials V1​,V2​ and V3​ respectively. The potential at ‘O' is

C1​+C2​+C3​C1​V1​+C2​V2​+C3​V3​​

C1​+C2​+C3​C1​V1​+C2​V2​−C3​V3​​

C1​+C2​+C3​C1​V1​−C2​V2​−C3​V3​​

C1​+C2​+C3​C1​V1​−C2​V2​+C3​V3​​