in a RLC or RC or RL circuit why do we need phasors to study the total potential?

Question

why not just apply kirchoff's law and add up the potentials across each passive circuit element. why do we need to calculate impedance to find out total potential across the circuit

Answer 1

In DC circuits that don't change in time one can just add up the potentials as you suggest. Also if nothing is changing in time the L's and the C's are not relevant.

In AC circuits the voltages are changing in time and the L's and the C's make a difference. One could do a full analysis and calculate what the voltage would be at every instant in time or one can do a simpler analysis that includes peak amplitude and phase angle (a phasor). This is actually much less complex because one does not have to calculate voltages at different instants in time.

In a AC system the voltage at any given time at a given point can be expressed as follows:

V = Vm sin( t/T + a )
where
V is the voltage at time t
Vm is the max voltage (is a constant)
t is time
T is period of the AC system
a is the phase angle

Were one must add two voltages it becomes

Vtot = Vm sin( t/T + a ) + Vn sin(t/T +b )

b is the phase angle of the second voltage
Vn is the max voltage (2nd voltage)

As you add more and more voltages it gets quite complex.

Phasors are much easier to deal with.

Vtot = Vm @ a + Vn @ b
(this is polar form -- to do the addition they have to be converted to rectangular form)

Note that the phasors have no trig function. This make the math more simple and it works.

Answer 2

Phasors imply there is a difference between things. In this case it is a time difference between the currents in R and C and L when the current fluctuates. (If no fluctuation, i.e. direct current, then impedance does not exist; a capacitor is just an open circuit and an inductor is just a low-value resistor equal to the copper resistance of the winding.)

So, with the current wiggling a bit, the C and L are not quite as "passive" as you think. The current and voltage are not in phase as they are in resistors. Because R has the current in phase and L is 90 degrees lagging and C is 90 degrees leading, there's a difference. The exception is if the impedance of L and C in a circuit are equal, they cancel each other (resonance) and act as a resistor does. In that case there is no difference between the resistor and the L/C combination at the resonant frequency. You could just sum them up like it was DC.

So just ask your teacher to make sure the driving signal for all your questions is the resonant frequency of the L/C, because life is complicated enough and you need to lower your blood pressure. Yeah, that will fly.

Answer 3

I THINK KIRCHOFF'S LAW IS APPLIED TO THE CIRCUITS WITH RESISTER ONLY .SO TO CALCULATE THE TOTALL IMPEDENCES IN THE RLC,RC,RL CIRCUITS WE USE PHASORS .

Answer 4

The jω operator is what makes a straight-forward use of Kirkoff's laws. Otherwise you end up trying to solve complex integrodifferential equations. V(i) = iR + Ldi/dt + (1/C)∫idt , for example, becomes V = I(R + jω + 1/(jωC) , and can be easily manipulated algebraically.