Question

In the below circuit, the value of $V_1$ is:

• A. 6 V
• B. 7 V
• C. 8 V
• D. 10 V

Hint:

When resistors are symmetrical around a battery in a parallel branch, the battery voltage is directly the drop across the branch.

Answer 1

The Correct Option is A

We are given a network with multiple voltage sources and resistors, and we need to determine the voltage $V_1$ across the 6V battery.
Let’s analyze the three branches in the circuit:
- Left branch: Contains an 8V battery in series with $2\ \Omega$ and $2\ \Omega$ resistors.
- Middle branch: Contains a $1\ \Omega$ resistor, a 6V battery (from top to bottom), and another $1\ \Omega$ resistor.
- Right branch: Contains a $3\ \Omega$ resistor and an 18V battery.
We are asked to find the potential across the battery in the middle branch, which is marked as $V_1$.
Let’s compare node voltages vertically across branches (since all branches are parallel):
In the middle branch, the 6V battery is between two $1\ \Omega$ resistors. The battery is oriented such that it adds 6V potential between the two points.
Due to symmetry and equal resistors (1$\Omega$ above and below), the voltage drop across the resistors is the same, and the battery just shifts the voltage across the node.
Hence, the voltage across $V_1$ equals the battery voltage, which is clearly: \[ \boxed{6V} \] So, the value of $V_1$ is 6V.