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(B) Let the potential at $A$ be $20 \ V$ and at $C$ be $0 \ V$. The circuit is symmetric. The potential at $B$ and $D$ can be found using nodal analys

Vedclass · Accepted Answer

Both the $4 \mu F$ capacitors carry equal charges in same sense.

Vedclass · Answer

(B) Let the potential at $A$ be $20 \ V$ and at $C$ be $0 \ V$. The circuit is symmetric. The potential at $B$ and $D$ can be found using nodal analysis. Let $V_B$ and $V_D$ be the potentials at nodes $B$ and $D$. Applying Kirchhoff's Current Law at node $B$: $(V_B - 20)/4 + (V_B - 0)/2 + (V_B - V_D)/2 = 0$. Multiplying by $4$,we get: $(V_B - 20) + 2V_B + 2(V_B - V_D) = 0 \implies 5V_B - 2V_D = 20$. Applying Kirchhoff's Current Law at node $D$: $(V_D - 20)/2 + (V_D - 0)/4 + (V_D - V_B)/2 = 0$. Multiplying by $4$,we get: $2(V_D - 20) + V_D + 2(V_D - V_B) = 0 \implies -2V_B + 5V_D = 40$. Solving the two equations: $V_B = 60/7 \ V$ and $V_D = 80/7 \ V$. Since $V_D > V_B$,$V_B - V_D The charge on the $4 \mu F$ capacitor connected to $A$ is $q_1 = 4(20 - V_B) = 4(20 - 60/7) = 4(80/7) = 320/7 \ \mu C$. The charge on the $4 \mu F$ capacitor connected to $C$ is $q_2 = 4(V_D - 0) = 4(80/7) = 320/7 \ \mu C$. Both capacitors carry equal charges in the same sense (from $A$ towards $B$ and from $D$ towards $C$). Thus,option $B$ is correct.

The figure shows a diagonal symmetric arrangement of capacitors and a battery. Identify the correct statements.

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