The number of junctions in the circuit is
Correct Answer :
6
Solution :
The correct option is 6.
Definition of a Junction:
In electrical circuit analysis, a junction (also known as a principal node) is defined as a point in the circuit where three or more circuit elements (such as resistors, capacitors, inductors, or voltage sources) meet.
Points where only two elements meet in series (such as the corners connecting a single source to a single resistor) are simple nodes, not junctions.
By carefully analyzing the provided circuit diagram, we can identify and locate the junctions as follows:
1. Left-Middle Junction:
Located on the left vertical wire, where three elements intersect: the top-left DC source (battery), the bottom-left inductor, and the horizontal wire containing the capacitor.
2. Top-Middle Junction:
Located on the top horizontal wire, where three elements intersect: the top-left resistor, the top-right resistor, and the vertical branch going down (which starts with a capacitor).
3. Bottom-Middle Junction:
Located on the bottom horizontal wire, where three elements intersect: the bottom-left battery branch, the bottom-right resistor, and the vertical branch containing the resistor.
4. Top-Right Junction:
Located at the top-right corner, where three elements intersect: the top-right resistor, the upper-right inductor, and the far-right capacitor branch.
5. Bottom-Right Junction:
Located at the bottom-right corner, where three elements intersect: the bottom-right resistor, the lower-right inductor, and the far-right capacitor branch.
6. Center-Right Combined Junction:
In the middle of the circuit, there is a center dot and a right-middle connection point. These two points are connected directly by a horizontal conducting wire with zero resistance (no electrical components in between). Therefore, they are at the same electrical potential and constitute a single electrical junction.
This combined junction connects five components: the middle-left capacitor, the upper-middle vertical resistor, the lower-middle vertical resistor, the upper-right inductor, and the lower-right inductor.
Counting all these distinct junctions, we have:
1 (Left-Middle) + 1 (Top-Middle) + 1 (Bottom-Middle) + 1 (Top-Right) + 1 (Bottom-Right) + 1 (Center-Right Combined) = 6 junctions.
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