Three uncharged capacitors of capacitances C_ | vedclass

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Question

(A) Let the potential at point $O$ be $V$. Since the capacitors were initially uncharged,the sum of charges on the plates connected to point $O$ must

Vedclass · Accepted Answer

$\frac{C_1 V_1 + C_2 V_2 + C_3 V_3}{C_1 + C_2 + C_3}$

Vedclass · Answer

(A) Let the potential at point $O$ be $V$. Since the capacitors were initially uncharged,the sum of charges on the plates connected to point $O$ must be zero (by the principle of conservation of charge).The charge on capacitor $C_1$ is $q_1 = C_1(V_1 - V)$.The charge on capacitor $C_2$ is $q_2 = C_2(V_2 - V)$.The charge on capacitor $C_3$ is $q_3 = C_3(V_3 - V)$.According to the conservation of charge at node $O$:$q_1 + q_2 + q_3 = 0$$C_1(V_1 - V) + C_2(V_2 - V) + C_3(V_3 - V) = 0$$C_1 V_1 - C_1 V + C_2 V_2 - C_2 V + C_3 V_3 - C_3 V = 0$$C_1 V_1 + C_2 V_2 + C_3 V_3 = V(C_1 + C_2 + C_3)$$V = \frac{C_1 V_1 + C_2 V_2 + C_3 V_3}{C_1 + C_2 + C_3}$

Three uncharged capacitors of capacitances $C_1$,$C_2$,and $C_3$ are connected as shown in the figure. If $A$,$B$,and $C$ are at potentials $V_1$,$V_2$,and $V_3$ respectively,then the potential at point $O$ is:

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