MHB How to find currents and voltages with 2 batteries connected?

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To analyze a circuit with two connected batteries, it's essential to redraw the schematic and label all currents and voltages across components. The current flows from the negative terminal to the positive terminal of the batteries. Participants suggest using mesh analysis for a systematic approach to determine the values. Alternatively, simplifying the circuit with equivalent components can help clarify the analysis. Ultimately, both methods can be effective depending on the complexity of the circuit.
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Assume that this circuit has been connected as shown for a very long time. Re-draw the schematic and label the currents and voltages in and across all components including the View attachment 4024batteries. All components are “ideal.”
 

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The current runs from the negative side of the battery to the postive correct? So first should I try and replace what I can with equivalent components to clean up the circuit?
or should try try and go ahead and use mesh analysis
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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