The voltage at A, B, C, and D are VA, VB, VC, and VD. The current through AC is i1 and the current through AD is i2. The total current is i.
Applying the nodal analysis law to VC:
(VC - VA)/5Ω + (VC - VD)/5Ω + (VC - VB)/10Ω = 0
(VC - 6)/5Ω + (VC - VD)/5Ω + VC/10Ω = 0
(1/5 + 1/5 + 1/10)VC - (1/5)VD = 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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