1. Resonant frequency of a series LCR circuit

For a series LCR circuit, the resonant frequency is

where:

• $L$ = inductance
• $C$ = capacitance

So, to increase $f_0$, we must decrease the quantity $\sqrt{LC}$, i.e. decrease either $L$ or $C$.

2. Check each option

Option A: source frequency should be increased

Changing the source frequency does not change the circuit’s natural resonant frequency. Resonant frequency depends only on $L$ and $C$.

So, A is incorrect.

Option B: another resistance should be added in series with the first resistance

Resistance does not appear in

Hence adding resistance does not increase resonant frequency.

So, B is incorrect.

Option C: another capacitor should be added in series with the first capacitor

If capacitors are added in series, the equivalent capacitance decreases:

Thus,

Since resonant frequency is

a smaller capacitance gives a larger resonant frequency.

So, C is correct.

Option D: source frequency should be decreased

Again, source frequency does not determine the resonant frequency of the circuit.

So, D is incorrect.

3. Final answer

The resonant frequency increases when the equivalent capacitance decreases, which happens by adding another capacitor in series.

$\boxed{\text{C}}$