LLMs have shown strong performance in data-rich domains such as programming, but their reliability in engineering tasks remains limited. Circuit analysis is particularly challenging because it requires both multimodal understanding and precise mathematical reasoning. This paper presents an enhanced end-to-end circuit problem-solving framework using Gemini 2.5 Pro as the backbone model for scalable engineering-education applications. We systematically evaluate Gemini 2.5 Pro on undergraduate circuit-analysis problems and identify two major failure modes: circuit-recognition hallucinations, especially source-polarity errors, and reasoning-process hallucinations, such as incorrect current-direction assumptions. To reduce recognition errors, we integrate a fine-tuned YOLO detector with OpenCV-based processing to isolate voltage and current sources for polarity re-identification. To mitigate reasoning errors, we introduce an ngspice-driven verification loop that supports iterative refinement with optional human feedback. On 83 problems, the proposed pipeline achieves 97.59% accuracy, compared with 79.52% for baseline Gemini. Across four hand-drawn diagram variations, accuracy improves from 60.61%--71.21% to 89.39%--92.42%, with statistically significant gains (p<0.005). On 43 problems from a different textbook, accuracy increases from 58.14% to 83.72%, further supporting cross-textbook generalizability. Error analysis shows that circuit recognition remains the dominant source of residual failures, particularly under varying diagram representations. Overall, the framework substantially improves the robustness, scalability, and generalizability of LLM-based circuit problem solving for engineering education and practical circuit analysis.

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