If an AC L-C circuit, which the inductor has internal resistance and given you root mean square voltage of VL, VC, Vrms and Irms of the circuit, and asking you to find the resistance of Inductor which is the internal one, can you find the resistance of inductor through this equation ? Z sqart(R^2 + (XL - XC)^2) ? and we find XL, XC and Impedance of the circuit through given voltage and current and so the resistance of the inductor is R sqart(Z^2 - (XL - XC)^2) is that correct ?
You know three 4 things (1) V(L) (2) V(C) (3) V(rms) (4) I(rms) You are not given neither omega ( frequency of a.c.) nor values of L and C and so you can not use Z sqrt(R^2 + (XL - XC)^2) since XL 2*pi*f*L and XC (1/2*pi*f*C) and so square this equation , because then we can do something Z sqrt(R^2 + (XL - XC)^2) Z^2 R^2 + (XL - XC)^2 multiply I(rms)^2 both sides. Consider I(rms) I (I*Z)^2 (IR)^2 + (I*(XL) - I(XC))^2 since V(rms) I*Z , V(R) I*R , V(L) I*XL and V(C) I*XC so [V(rms)]^2 [V(R)]^2 + [V(L) - V(C)]^2 you are given V(rms) , V(L) and V(C) so you can find V(R) and after since V(R) I(internal resistance R) you know V(R) and I I(rms) so you can find R. NOTE: If this helps you please remember to vote Best Answer.
