Questions: Kirchhoff's Current Law (KCL)

Question 1

Three branches meet at a node. I₁ = 4 A flows into the node and I₂ = 7 A flows into the node. I₃ is defined as flowing out of the node. What is I₃?

• A. 3 A (I₂ − I₁)
• B. −11 A (indicating current flows inward)
• C. 11 A (I₁ + I₂ must leave)
• D. It cannot be determined without knowing the resistances

Answer: (C)

KCL states that current entering a node equals current leaving it. I₁ + I₂ = 4 + 7 = 11 A enters, so 11 A must leave through I₃. Option D is wrong because KCL is independent of resistances — it's a conservation law, not Ohm's law. Option B would be correct if I₃ were defined as entering (the solution being negative would mean it actually exits), but since I₃ is defined as leaving, the answer is simply +11 A.

Question 2

Which physical principle directly underlies KCL?

• A. Conservation of energy — total power delivered to a node must equal zero
• B. Conservation of charge — charge cannot accumulate at a node in steady state
• C. Ohm's law — current at a node is proportional to the local voltage
• D. Conservation of momentum — the net force on charge carriers at a junction is zero

Answer: (B)

KCL is a direct consequence of charge conservation. In steady-state circuit operation, charge cannot pile up at a node — every coulomb that flows in must flow out. This is entirely independent of what circuit elements are present. Ohm's law (option C) relates current to voltage within a resistor; it's a material property, not a conservation law, and is not what KCL expresses.

Question 3

If you assign a reference direction to a branch current and the circuit solution yields a negative value for that current, the result is invalid and you is expected to re-assign the direction.

• T. True
• F. False

Answer: False

A negative value is perfectly valid — it simply means the actual current flows opposite to your chosen reference direction. This is one of the strengths of KCL-based analysis: you can assign reference directions arbitrarily, write the equations, solve, and let the algebra determine the true direction. Requiring re-assignment would destroy the systematic algebraic approach and is not necessary.

Question 4

In a circuit, a resistor 'uses up' some of the current flowing through it, so the current exiting a resistor is less than the current entering it.

• T. True
• F. False

Answer: False

This is one of the most persistent misconceptions in introductory circuits. Resistors do not consume current — they convert electrical energy into heat, but the same current that enters a resistor exits it. What the resistor does consume is voltage (electrical potential energy). KCL guarantees that current is conserved at every node, including both terminals of a resistor. A light bulb glowing brightly has the same current flowing in and out; it's the voltage drop (and thus power P = IV) that represents energy dissipation.

Question 5

Explain why the sum of all currents at a node must equal zero, using the concept of charge conservation.

Model answer: A node is a connection point with no capacity to store charge. If more charge flowed in than out over any time interval, charge would accumulate at the node — but this doesn't happen in steady-state operation. Since charge is conserved and cannot pile up, the rate of charge flowing in must equal the rate flowing out. Current is defined as charge per unit time (I = dq/dt), so equal charge flow rates mean equal currents. Expressing this with a sign convention (positive for entering, negative for leaving), the algebraic sum of all branch currents at any node equals zero.

The argument generalizes beyond steady state through charge neutrality: in normal circuit conductors, charge accumulation would build up an electric field that opposes further accumulation, making the transient extremely short-lived. KCL is therefore an excellent approximation for any circuit analysis at frequencies well below those where capacitive effects at wire junctions matter.