The voltage \(V\) in the given figure is equal to :
Show Hint
While applying KVL:
• Carefully track source polarities.
• A wrong polarity sign changes the final answer.
• Always compare the calculated polarity with the polarity marked in the question.
Concept:
Kirchhoff’s Voltage Law (KVL) states that:
\[
\sum V = 0
\]
around any closed loop.
While traversing a circuit:
• Crossing from negative to positive terminal gives voltage rise.
• Crossing from positive to negative terminal gives voltage drop.
Proper attention to source polarity is extremely important while solving circuit voltage problems.
Step 1: Choose the loop direction.
We traverse the loop clockwise.
The circuit contains:
• A \(5V\) source on the left
• A \(4V\) source on the top
• Another \(4V\) source on the right
• A resistor branch where voltage \(V\) is defined
Step 2: Apply polarity signs carefully.
Traversing clockwise:
• Across the left \(5V\) source:
\[
+5V
\]
because we move from negative to positive terminal.
• Across the top \(4V\) source:
\[
-4V
\]
because we move from positive to negative terminal.
• Across the right \(4V\) source:
\[
-4V
\]
because traversal goes from positive to negative terminal.
Step 3: Apply Kirchhoff's Voltage Law.
Using KVL:
\[
+5-4-4+V=0
\]
Simplifying:
\[
5-8+V=0
\]
\[
-3+V=0
\]
\[
V=3V
\]
However, the polarity marked across the resistor indicates:
\[
+V-
\]
which is opposite to the assumed current direction during traversal.
Therefore:
\[
V=-3V
\]
Step 4: Write the final answer.
Hence, the required voltage is:
\[
\boxed{-3V}
\]
Therefore, the correct option is:
\[
\boxed{(B)\ -3V}
\]
