Question

The potential difference between $A$ and $B$ in the following situation is:

Answer 1

In this question, we need to find the potential difference between points $A$ and $B$ . To solve this, first select a point and assume the potential to be $0{\text{ V}}$ at that point. After that, find out the current in all the branches of the circuit using Kirchhoff’s current law and then write down the voltage across each component of the circuit and then subtract the voltages between the required points to find the potential difference.

Complete step by step solution:
Let us assume the potential at point A be $0{\text{ V}}$
Let the current through ${\text{DF}}$ branch be ${I_1}$ and through ${\text{FB}}$ branch be ${I_2}$

Now, applying Kirchhoff’s current law at point $B$
As the total current entering a junction or node must be equal to the current leaving the node
Thus, ${I_2} = 3 + 4$
$\Rightarrow {I_2} = 7{\text{ A}}$
Similarly applying Kirchhoff’s current law at point $F$ we get,
$5 + {I_1} = 7$
$\Rightarrow {I_1} = 2{\text{ A}}$ towards the point $F$
Now, since we got current through all the branches write down the potential drop across each component

Potential drop across the ${\text{2 }}\Omega$ resistor is $2 \times 5 = 10{\text{ V}}$
Potential drop across the battery should be $10{\text{ V}}$
Since point $F$ is connected to the negative terminal of battery potential at point $F$ is $0{\text{ V}}$
Current passing through ${\text{1 }}\Omega$ resistor is $7{\text{ A}}$
Potential drop across the ${\text{1 }}\Omega$ resistor will be $7{\text{ V}}$
Since current flows in a resistor from higher potential to lower potential, potential at point ${\text{G}}$ is $- 7{\text{ V}}$
Potential drop across battery must be ${\text{5 V}}$
Thus, ${{\text{V}}_G} - {V_B} = 5$
$- 7 - {V_B} = 5$
$\Rightarrow {V_B} = - 12{\text{ V}}$
Potential difference between $A$ and $B$ is given by ${{\text{V}}_A} - {V_B}$
Substituting the values,
$\Rightarrow 0 - \left( { - 12} \right)$
$\Rightarrow {{\text{V}}_A} - {V_B} = 12{\text{ V}}$
The Potential difference between $A$ and $B$ is $12{\text{ V}}$.

Note:
To solve this type of question we can choose only one point at zero potential and must write all other potential in reference to it. We cannot take two points at zero potential thus one must choose the zero potential point such that the question can be solved easily.
In a resistor, current flows from higher potential to lower potential and in a battery, current flows from lower potential to higher potential. If the current flows in the opposite direction in a battery the battery is said to be charging.