A student is investigating the resonance behaviour of a series LCR circuit in the laboratory. The inductance L, capacitance C and resistance R can each be varied independently.
a. (i) Explain why the resonant angular frequency of the circuit depends only on L and C but not on R. Provide physical reasoning based on the definition of resonance.
b. (ii) If the capacitance of the circuit is increased while L and R are kept unchanged, qualitatively describe how the resonant frequency will be affected and justify your answer.
c. (iii) Suppose the capacitance is suddenly halved with L fixed. Without performing a numerical calculation, state how the resonant frequency will change and support your answer with suitable reasoning.