Final answer:
At the resonant frequency in a series RLC circuit, the voltage across both the inductor and the capacitor can be large due to magnification, but their combined reactive voltages cancel each other out, resulting in a net voltage of zero across them when considered together.
Step-by-step explanation:
The voltage across an inductor and a capacitor in a series RLC circuit at the resonant frequency is such that the reactive components have equal and opposite impedances, causing them to cancel each other out. At resonance, the inductor's and capacitor's reactance are equal in magnitude but opposite in sign, resulting in a net reactive impedance of zero. The voltage across both the inductor and the capacitor can be much larger than the supply voltage due to the Q factor of the circuit, which can cause a voltage magnification effect at resonance. However, the net voltage considering both components is zero since they are 180 degrees out of phase with each other. The resonance frequency (ωR) of a series RLC circuit is given by the formula ωR = 1 / √(LC), which is the frequency at which this circuit will exhibit resonance behaviour.