8. Kirchoff’s first law (∑ i =0 ) and second law (∑ iR = ∑ E), where the symbols have their usual
meanings, are based on which laws respectively:
a.Conservation of charge, conservation of energy
b.Conservation of charge, conservation of momentum
c.Conversation of energy, conservation of momentum
d.None of the above

Correct Answer

Option a. Conservation of charge, conservation of energy precisely identifies the physical principles underlying Kirchhoff’s laws. Kirchhoff’s first law (KCL: ∑i=0 at junction) reflects charge conservation—total current entering equals total leaving, as charge cannot accumulate or vanish at a node. Second law (KVL: ∑iR=∑E around loop) embodies energy conservation—net voltage drop equals supplied emf, ensuring no energy creation/destruction in closed path.​

Option Analysis

• a. Conservation of charge, conservation of energy: Correct pairing. KCL derives from charge continuity (∑i=0 prevents charge buildup); KVL from electrostatic equilibrium (potential energy balance).​

• b. Conservation of charge, conservation of momentum: First correct (charge), but momentum irrelevant—circuits lack net momentum transfer; currents represent charge flow, not mechanical motion.​

• c. Conservation of energy, conservation of momentum: Both wrong—reverses laws and includes inapplicable momentum conservation.​

• d. None of the above: Incorrect, as option a accurately describes established physics foundations.​

Key Concepts

Kirchhoff’s Current Law (KCL) states algebraic sum of currents at junction equals zero: $\sum i=0$, directly from charge conservation since $i=dq/dt$. Kirchhoff’s Voltage Law (KVL) mandates $\sum iR=\sum E$ in loops, equivalent to $\sum V=0$, ensuring work around closed path vanishes per energy conservation. These laws enable complex circuit analysis beyond series/parallel rules, fundamental for CSIR NET electrical circuits. Applied universally in lumped circuits assuming steady-state conditions.​