Voltage at Test Node

Electricity and Magnetism Level 3

The electrical network shown above consists of ideal DC voltage sources and resistors. The negative terminals of the batteries are connected together, and the resistors are all connected together at a test node. What is the voltage at the test node relative to the negative bus (to 3 decimal places)?


The answer is 2.449.

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Steven Chase by Steven Chase , 37, USA

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1 solution

Steven Chase
Oct 17, 2016

Per Kirchoff's Node Law , the currents into the test node must sum to zero. Use Ohm's Law to calculate the currents into the nodes.

I n o d e = 1 − V n o d e 1 + 2 − V n o d e 2 + 3 − V n o d e 3 + 4 − V n o d e 4 + 5 − V n o d e 5 + 6 − V n o d e 6 = 0 I_{node} = \frac{1-V_{node}}{1} + \frac{2-V_{node}}{2} + \frac{3-V_{node}}{3} + \frac{4-V_{node}}{4} + \frac{5-V_{node}}{5} + \frac{6-V_{node}}{6} = 0

6 = V n o d e ( 1 1 + 1 2 + 1 3 + 1 4 + 1 5 + 1 6 ) 6 = V_{node}(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6})

V n o d e ≈ 2.449 V_{node} \approx 2.449

3 Helpful 1 Interesting 1 Brilliant 0 Confused

@Steven Chase hello.
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Approximately how much he/she can able to earn??

Talulah Riley - 9 months, 3 weeks ago

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