# How does current/component voltage phase difference calculated in pure circuits remain the same for mixed circuits?

In class, we derived the phase difference values between the component voltage and the circuit current for pure inductive and capacitive circuits. Later, while doing LR, RC, and LC circuits, we used the same phase lag values to draw the phasor diagrams outright, without starting all over again.

(1) How can we assume that the phase difference values calculated for pure circuits remain the same for mixed circuits?

(2) Also, why can we not add the component voltages to get source voltage in mixed series circuits? For example, in an LR circuit, why can't you add $$V_R$$ and $$V_L$$ to get $$E{source}$$?

• On adding $V_r$ and $V_l$; I meant to ask whether adding the whole thing, not the amplitudes; as in, If $V_r= V_{r(0)}sin(\omega_1 t)$ and $V_l= V_{l(0)}sin(\omega_2 t)$, can I add both? Not the amplitudes- the whole thing, with the sines. Mar 1 at 11:42