**Category:** Electromagnetism  
**Subtype:** Oscillating Circuits (LC Circuits)  
**Problem Description:** This problem involves an ideal oscillating circuit undergoing free electromagnetic oscillations. The charge on a capacitor varies according to the equation \(q=Q_{0} \cos \left(\frac{2 \pi \cdot 10^{-6}}{3} t+\varphi\right)\). The task is to determine the amount of charge \(\Delta q_{3}\) that passes through a cross-section of the conductor during a specific time interval, given the charge transferred in previous intervals.  

**Key Points:**  
- The problem provides the charge transferred over three time intervals: \(\Delta t_{1} = 0.5 \mu s\), \(\Delta t_{2} = 1 \mu s\), and \(\Delta t_{3} = 1 \mu s\).  
- The charges transferred in the first two intervals are given as \(\Delta q_{1} = 3 \cdot 10^{-6} C\) and \(\Delta q_{2} = 9 \cdot 10^{-6} C\).  
- The goal is to find the value of \(\Delta q_{3}\) from the provided options.  

**Objective:** Find the charge \(\Delta q_{3}\) that passes through the conductor during the third time interval.