Final answer:
The statement is false because the voltages across the resistor, inductor, and capacitor in an AC circuit do not simply add up to the source voltage amplitude, due to phase differences requiring vector addition.
Step-by-step explanation:
The statement that "in an AC circuit, the amplitudes of VR (voltage across the resistor), VL (voltage across the inductor) and VC (voltage across the capacitor) always add up to the amplitude of Vsource" is false. In an AC circuit, VR is in phase with the current, while VL leads and VC lags the current by 90 degrees each.
This results in VL and VC being out of phase with each other by 180 degrees. Therefore, when these voltages are added vectorially, they partially cancel each other out if they have the same magnitude and don't sum up directly to the source voltage amplitude. The actual relationship between the source voltage and the voltages across R, L, and C in an AC circuit requires vector addition due to phase differences.
The statement that in an AC circuit, the amplitudes of VR, VL, and VC always add up to the amplitude of Vsource is false.
While VR is in phase with the current, V₁ leads by 90°, and Vc follows by 90°. Thus VL and Vc are 180° out of phase (crest to trough) and tend to cancel, although not completely unless they have the same magnitude. Since the peak voltages are not aligned (not in phase), the peak voltage Vo of the source does not equal the sum of the peak voltages across R, L, and C.
The actual relationship is given by the Kirchhoff's loop rule, which states that the total voltage around the circuit Vo is equivalent to the sum of VR, VL, and VC.