STAR connection

StarConnection
Three batteries have their negative terminals connected together.
Find the voltage read by an ideal voltmeter.

Solution.

We assume that the potential of the point A is zero. Then, the potential of the point D is 3V, the potential of the point E is 6V and the potential of the point C is 9V. We can denote the potential of the point B as VB.

The voltage VDB on the resistor is 3 – VB and the current equals (3 – VB)/100
and the voltage VEB on the resistor is 6 – VB and the current equals (6 – VB)/100.
Also, the voltage VCB on the resistor is 9 – VB and the current equals (9 – VB)/200.

According to Kirchhoff’s current law, at any instant, the algebraic sum of the currents entering a node in the circuit is zero.

Thereby,

(3 – VB)/100 + (6 – VB)/100 + (9 – VB)/200 = 0

6 – 2VB + 12 – 2VB + 9 – VB = 0

5VB = 27

VB = 5.4V

Finally, the voltage read by an ideal voltmeter is 5.4V.

 
 

 

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