Series Resistor Circuit Voltage (2 Power Sources)

[daba]

Now down to the nitty-gritty....

In the OP's circuit, the assumption is made that the positive of the 2 batteries will be the stated voltages, but in actual fact the 12V battery will attempt to charge the 9V battery, at a current that we cannot determine because we don't know its internal resistance. It is most likely that the pos. terminal of the 9V battery will be some potential above 9V, and thinking further, it would have to be to cause current to flow in reverse through it. We have to have 20uA flowing right to left to get the voltages we calculate, and I doubt that will be true, because we've ignored the internal resistance to a reverse current in the 9V battery.

There's going to be a substantial difference between the theoretical voltage at point B, and anything you might measure, due solely to the characteristics of the 9V battery, everything else is a known factor.

Since it was an exam question originally, let's stick with the theoretical and not throw unknowns into the equation.

 

[kallileo]

Assuming the current is flowing CW:
+9V-74*I-76*I-12V=0
I=-0,02A thus the current is flowing CCW.

VB+76*I-12V=0
VB=10,48V

 

[ebolbol]

Both power sources share a common negative, so the voltage difference is only 3 volts.
That 3 volts is dropped across the total of all 4 resistors with a total value of 150k ohms.
Point B is very close to mid point of resistor values R1 plus R2 equal 74k ohms,
and R3 plus R4 equal 76k ohms , so at point B it equals 1.48volts above 9 volts.
Result being 10.48 volts at point B above earth

The question was "Calculate the voltage at point B in the given circuit."

That is impossible to answer, because the question does not specify what reference for the voltage should be taken.

To be pedantic, it would have been better if the question had been worded "Calculate the potential at point B in the given circuit.". At least that would infer a voltage above ground potential....

I personally hate questions that are given in exams or tests that do not meet one very simple criteria.....

"Is the question ambiguous" - of course in this case it is. You have to make an assumption that the questioner means "with respect to ground potential", but he didn't say so.

Anyway, enough ramblings about the question, the answer is 10.48V "above ground potential"

It is easy to calculate...

Total Potential Difference (wrt ground) across the four resistors = 3V

Total Resistance = 47K + 27K + 56K + 20K = 150K

Current through all resistors = V/R = 3/150000 = 0.00002 A

Volt drop across the 47K resistor = 0.94V
Volt drop across the 27K resistor = 0.54V
Volt drop across the 56K resistor = 1.12V
Volt drop across the 20K resistor = 0.40V

Either way you look at it the potential, above ground, at point B is...

9 + 0.94 + 0.54 = 10.48

or,

12 - 0.40 - 1.12 = 10.48

The two individuals above have convincingly answered this question the correct answer is 10.48V

No further due

 

[John Morris]

Georg Simon Ohm has rolled over in his grave 63 times.

 

[ebolbol]

Georg Simon Ohm has rolled over in his grave 63 times.

LOL to the response as well as quoted signatures!!!

How true it is

 

[daba]

Georg Simon Ohm has rolled over in his grave 63 times.

Are those roll-overs w.r.t. earth ?

 

[ebolbol]

Are those roll-overs w.r.t. earth ?

Again....LOL!