Step 1: Understanding the Concept:
Electrical resonance occurs in an AC series RLC circuit when the inductive reactance ($X_L$) exactly cancels out the capacitive reactance ($X_C$), making the circuit purely resistive.
The frequency at which this happens is the resonant frequency.
Step 2: Key Formula or Approach:
The condition for resonance is $X_L = X_C$.
Since $X_L = \omega L = 2\pi f L$ and $X_C = \frac{1}{\omega C} = \frac{1}{2\pi f C}$, we equate them:
\[ 2\pi f_r L = \frac{1}{2\pi f_r C} \]
Solving for the resonant frequency $f_r$:
\[ f_r = \frac{1}{2\pi \sqrt{LC}} \]
Step 3: Detailed Explanation:
Looking at the formula for resonant frequency, $f_r = \frac{1}{2\pi \sqrt{LC}}$, it is evident that the resonant frequency depends solely on the values of the inductance ($L$) and the capacitance ($C$).
The formula contains no term for the resistance ($R$).
Therefore, changing the resistance to $\frac{1}{3}\text{rd}$ of its original value (or any other value) will have absolutely no effect on the point of resonance. It will change the sharpness (Q-factor) of the resonance and the maximum current, but not the frequency at which it occurs.
Step 4: Final Answer:
The resonant frequency remains unchanged.