Kirchhoff Loop and Nodal Analysis
Kirchhoff's voltage law is the algebraic sum of potential changes around any lumped-circuit loop. Combine independent loop equations with junction equations to solve multi-source networks.
Why this shows up in the exam
Multi-loop resistor networks · Potential difference between two nodes · Circuits with several batteries
Learn the idea
Around a closed loop, potential rises and drops sum to zero. Returning to the same point returns to the same electric potential. Battery polarity sets rises or drops; resistor signs depend on whether the traversal follows or opposes current.
🧠 Memory hook: Walk a loop once and keep every sign tied to the walk.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- sum Delta V_loop = 0 — energy-conservation loop equation
- Delta V_R = -IR along current — resistor drop during traversal with current
- Delta V_source = +E from minus to plus — ideal-source rise by polarity
How to approach it
- 1Assign branch currents
- 2Write KCL and independent KVL equations
- 3Solve algebraically and interpret signs
Common slip-ups that cost marks
- •Changing the assumed current while writing equations
- •Using emf sign from current instead of polarity
- •Writing dependent loops only
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A cell of emf 6 V and internal resistance 1 ohm is connected to a 2 ohm resistor. Find the circuit current.
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