Question

In the given circuit, find the potential difference between \( A \) and \( B \). 
 

Hint:

For circuits with parallel branches, the potential difference between two points is primarily influenced by the voltage sources in the branches. Consider the highest voltage source when resistances are equal.

Answer 1

The circuit consists of three branches connected between points \( A \) and \( B \), each having a \( 1 \, \Omega \) resistor in series with voltage sources of \( 3 \, \mathrm{V} \), \( 2 \, \mathrm{V} \), and \( 1 \, \mathrm{V} \), respectively. The current in each branch can be calculated using Ohm's Law: \[ I = \frac{\text{Voltage}}{\text{Resistance}}. \] \begin{itemize} \item For the top branch: \( I_1 = \frac{3}{1} = 3 \, \mathrm{A} \), \item For the middle branch: \( I_2 = \frac{2}{1} = 2 \, \mathrm{A} \), \item For the bottom branch: \( I_3 = \frac{1}{1} = 1 \, \mathrm{A} \). \end{itemize} Since all resistances are equal, the potential difference between \( A \) and \( B \) is determined by the branch with the highest voltage source. Hence, \[ V_{AB} = 3 \, \mathrm{V}. \]