Single-resistor series example — consider a simple circuit with one ideal resistor R1 connected directly across an ideal 10 V DC source. What is the voltage across R1?

Introduction / Context:
This problem reinforces the idea that in a one-element series circuit, the entire source voltage appears across that element. It is a direct application of Kirchhoff’s Voltage Law (KVL) and Ohm’s law and sets the stage for understanding voltage division when more than one element is present.

Given Data / Assumptions:

• Ideal 10 V DC source.
• Only one component in the loop: resistor R1.
• Ideal wires, no internal source resistance.

Concept / Approach:
KVL states that the algebraic sum of voltages around any closed loop is zero. With a single resistor in the loop, the resistor must drop the full source voltage to satisfy KVL. Ohm’s law relates current and resistance, but the drop is set by the source magnitude because there are no other elements to share it.

Step-by-Step Solution:

Verification / Alternative check:
Measure with an ideal voltmeter connected across R1; it reads the node-to-node source voltage because the resistor is directly across the source terminals.

Why Other Options Are Wrong:

Common Pitfalls:
Assuming “voltage division” always applies; it only applies when multiple series elements share the source voltage.

Final Answer:
10 V