A 10 V voltage source V1 connects to node A through R1 = 10 Ω, a 5 V voltage source V2 connects to the same node A through R2 = 10 Ω, and a resistor R3 = 10 Ω connects node A to ground. The negative terminals of both sources are grounded. What is the voltage at node A?

Answer: B. 5 V

Using superposition, consider one voltage source at a time with the other shorted. With V1 alone, R2 and R3 in parallel make 5 Ω, so node A is at 10 V × 5/(10 + 5) ≈ 3.33 V. With V2 alone, likewise, 5 V × 5/(10 + 5) ≈ 1.67 V. Together they give 3.33 + 1.67 = 5 V, and R3 carries 5 V/10 Ω = 0.5 A. Superposition holds for linear circuits and cannot be applied directly to squared quantities such as power.

• A. 7.5 V is the node voltage if R3 were absent.
• B. Correct. 3.33 V + 1.67 V = 5 V.
• C. About 3.3 V is the contribution of V1 alone, without adding V2's 1.67 V.