**(A)**

The voltage at A, B, C, and D are V_{A}, V_{B}, V_{C}, and V_{D}. The current through AC is i_{1} and the current through AD is i_{2}. The total current is i.

Applying the nodal analysis law to V_{C}:

(V_{C} - V_{A})/5Ω + (V_{C} - V_{D})/5Ω + (V_{C} - V_{B})/10Ω = 0

(V_{C} - 6)/5Ω + (V_{C} - V_{D})/5Ω + V_{C}/10Ω = 0

(1/5 + 1/5 + 1/10)V_{C} - (1/5)V_{D} = 6/5

What is the current through the battery in the circuit shown below? What is the equivalent resistance between A and B for the network of resistors?

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