Using the current-divider formula: You can directly compute the current in any branch of a series–parallel circuit from the current-divider rule without prior reduction. True or false?

Introduction / Context:
The current-divider formula is a convenient shortcut for parallel branches that share the same two nodes. However, many real circuits are series–parallel combinations, not a single simple parallel block. Knowing when the divider applies prevents calculation errors.

Given Data / Assumptions:

• Series–parallel circuits may contain multiple nodes and nested combinations.
• The current-divider rule applies only to elements in a single, pure parallel set connected to the same two nodes with a known total current entering the set.
• Other parts of the network may alter the currents unless the network is simplified first.

Concept / Approach:

To use the current-divider rule, first isolate a parallel group by reducing surrounding series parts or using Thevenin/Norton equivalents. Only then does the formula I_branch = I_total * (R_other / (R_branch + R_other)) (for two branches) hold. Applying it directly to arbitrary branches in a series–parallel network leads to incorrect results.

Step-by-Step Solution:

Verification / Alternative check:

Cross-check with nodal analysis: if the two elements do not share the exact same nodes, the divider rule is invalid. Nodal equations will show different node voltages, proving the shortcut does not apply.

Why Other Options Are Wrong:

• Selecting “True” overgeneralizes a special-case formula and ignores the need to first identify a single parallel set.

Common Pitfalls:

Applying the divider across elements separated by intervening series components; forgetting that dependent sources or reactive elements change the conditions for simple resistive dividers.

Final Answer:

False