Direct measurement across a single resistor — in the network, resistor R3 alone is connected between nodes A and B (no other elements in parallel with it). If the measured voltage between A and B is 9 V, what is the voltage across R3 (VR3)?

Introduction / Context:When a single element is the only component connected between two nodes, the element voltage equals the node-to-node voltage by definition. This is a straightforward but very common situation when taking measurements on boards and in simulations.

Given Data / Assumptions:

• R3 is the only component connected directly between nodes A and B.
• The measured node voltage difference is V_AB = 9 V.
• No additional parallel paths exist across A–B.

Concept / Approach:Element voltage is the potential difference between its terminals. If those terminals are exactly nodes A and B, then the element voltage equals V_AB. No knowledge of resistance value or currents is needed to equate VR3 with the measured A–B voltage in this configuration.

Step-by-Step Solution:

Verification / Alternative check:Use an ideal voltmeter directly across R3; it reads the same 9 V as the A–B measurement because it is the same two points.

Why Other Options Are Wrong:

Common Pitfalls:Misidentifying what nodes an element actually connects to; reversing polarity sign conventions (magnitude remains 9 V either way).

Final Answer:9 V