# 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 $$E{source}$$?

## 1 Answer

You may derive the phase difference in mixed circuits using complex numbers.

You CAN add Vr and Vl to get Esource, but all values have to be at the same instance. You can't simply add their amplitudes as they are out phase. So you have to use vector addition(phasor is based on concept of vectors) to calculate the source voltage.

• 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
• Yes, you can add both and you will surely get the correct value of the source voltage. You may take the help of a calculator and try a general case. Mar 2 at 12:06