**Category:** Electromagnetism

**Subtype:** Alternating Current (AC) Circuits

**Problem Description:** This problem involves analyzing an RLC (Resistor, Inductor, Capacitor) series circuit under an alternating voltage. The goal is to find the power factor (cosine of the phase difference) of the circuit based on the given voltage and current equations. 

**Key Elements:**
- The voltage across the circuit is given as \(u=U_{0} \cos \left(100 \pi t+\frac{\pi}{6}\right) V\).
- The current through the circuit is given as \(i=I_{0} \cos \left(100 \pi t-\frac{\pi}{12}\right) A\).
- The phase difference between the voltage and current needs to be determined to calculate the power factor.

**Objective:** Find the power factor of the RLC circuit from the provided voltage and current equations.