In the given circuit, if the potential at point B is 24 V, the potential at point A is:
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When dealing with series circuits involving multiple sources, always ensure the net voltage is calculated by considering the direction of each battery and the direction of current flow based on conventional current (from positive to negative terminal).
First, identify the direction of current flow, which must go from higher to lower potential, considering the battery orientations and resistances.
Step 1: Calculate the total voltage and resistance in the loop:
The voltages from the batteries add up since they are in series but opposing. \(12V\) battery opposes the \(36V\) battery, hence the net voltage is:
\[
V_{{net}} = 36V - 12V = 24V
\]
Step 2: Calculate the total resistance in the loop:
\[
R_{{total}} = 3\Omega + 2\Omega = 5\Omega
\]
Step 3: Calculate the total current using Ohm’s law (\(I = \frac{V}{R}\)):
\[
I = \frac{24V}{5\Omega} = 4.8A
\]
Step 4: Determine the voltage at point A:
Starting from B at \(24V\) and moving against the current through a \(3\Omega\) resistor, the voltage drop is:
\[
\Delta V = I \times R = 4.8A \times 3\Omega = 14.4V
\]
So, the potential at A is:
\[
V_A = V_B - \Delta V = 24V - 14.4V = 9.6V
\]
This implies a need to adjust the batteries' arrangement or calculations based on further details or corrections in the provided information or circuit diagram.
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