Kirchhoff’s Laws — A/L Physics

What must I remember about Kirchhoff’s Laws?

• Kirchhoff's First Law (Current Law / Junction Rule, KCL): The algebraic sum of currents meeting at ANY junction in an electrical circuit is identically zero: ∑ I_in = ∑ I_out; direct manifestation of Conservation of Electric Charge.
• Kirchhoff's Second Law (Voltage Law / Loop Rule, KVL): In ANY closed loop of an electrical network, the algebraic sum of electromotive forces equals the algebraic sum of the products of current and resistance (potential drops): ∑ E = ∑ (I R); direct manifestation of Conservation of Energy.
• Sign Conventions in KVL: Traverse loop in chosen direction (clockwise or anticlockwise): Source emf is positive when traversing from (-) to (+) terminal; Potential drop across resistor is positive (I R) when traversing in the direction of assumed current.
• Application to Multiloop Networks: For a network with N junctions and B branches, KCL provides (N - 1) independent junction equations, and KVL provides B - (N - 1) independent loop equations, yielding a fully solvable linear system.

Test yourself (1 minute)

1. Linear independence of loops

   When applying KVL to multiple loops, ensure each new loop includes at least ONE new branch not contained in previous loops to maintain mathematical independence.

2. Handling internal resistances in KVL

   Always treat internal resistance r as a series resistor physically attached to the cell: loop equation includes I * r.

3. Negative current result

   If solving circuit equations yields a negative value for current (I < 0), the magnitude is physically correct, but the true current flows in the OPPOSITE direction to your initial assumed arrow.

Practise Kirchhoff’s Laws questions today

Source: NIE G.C.E. (A/L) Physics Resource Book - Unit 7: Current Electricity

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Where does Kirchhoff’s Laws fit in the syllabus?

Unit 7.5 · Year 2 · Term 1