Instantaneous direction matters: If two time-varying currents flow in the same direction through a single branch at an instant, what is the instantaneous net branch current?

Introduction / Context:
Superposition and current addition are foundational concepts in circuit theory. In practical signal paths, multiple sources (or coupled subcircuits) can drive current through the same branch. Understanding how instantaneous currents combine ensures correct sizing of components and accurate waveform analysis.

Given Data / Assumptions:

• Two currents, i1(t) and i2(t), exist in the same branch at the same instant.
• Their directions at that instant are the same (defined by the same reference direction).
• Linear network behavior is assumed for superposition reasoning, but instantaneous algebra applies generally.

Concept / Approach:

Currents are signed quantities. When two currents share the same direction at an instant, their instantaneous values add arithmetically. The net branch current equals i_net(t) = i1(t) + i2(t). If one were opposite in direction, it would subtract based on the chosen sign convention.

Step-by-Step Solution:

Verification / Alternative check:

Kirchhoff's Current Law (KCL) at any node confirms current conservation. In a series branch, currents must be equal through elements; when multiple source contributions are present, they superimpose linearly with signs set by direction.

Why Other Options Are Wrong:

'Difference' applies only when currents are in opposite directions under the chosen sign. 'Zero' would require equal magnitudes but opposite directions. 'Cannot be determined' is incorrect because direction and magnitudes at the instant uniquely define the sum.

Common Pitfalls:

Mixing phasor addition with instantaneous addition; forgetting to apply consistent sign conventions; assuming RMS values can be simply added without considering phase.

Final Answer:

is the sum of the two currents