You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.
system
<image>Consider the capacitor shown in  <image 1>. The capacitance C(t) is given by $C(t) = C_0 (1 + 0.5 sin t)$. The voltage across this capacitor is given by $v(t) = 2 sin wt$ Find the current through the capacitor.
A. $C_0 sin wt cos t + 2w C_0 cos wt (1 + 0.5 sin t)$
B. $C_0 cos wt cos t + 2w C_0 sin wt (1 + 0.5 sin t)$
C. $C_0 sin wt cos t + 4w C_0 cos wt (1 + sin t)$
D. $C_0 sin wt cos t + 2w C_0 cos wt (1 - sin t)$

Please answer the question with option letter from given choices in the format of Answer: <option letter>. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. Please answer the final answer within the <answer> </answer> tags.
user
A
Consider the capacitor shown in  <image 1>. The capacitance C(t) is given by $C(t) = C_0 (1 + 0.5 sin t)$. The voltage across this capacitor is given by $v(t) = 2 sin wt$ Find the current through the capacitor.
A. $C_0 sin wt cos t + 2w C_0 cos wt (1 + 0.5 sin t)$
B. $C_0 cos wt cos t + 2w C_0 sin wt (1 + 0.5 sin t)$
C. $C_0 sin wt cos t + 4w C_0 cos wt (1 + sin t)$
D. $C_0 sin wt cos t + 2w C_0 cos wt (1 - sin t)$

Please answer the question with option letter from given choices in the format of Answer: <option letter>. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. Please answer the final answer within the <answer> </answer> tags.
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