# Why does phase shift occur?

Discussion in 'General Electronics Chat' started by jmsparkland1, Mar 5, 2012.

1. ### jmsparkland1 Thread Starter New Member

Feb 29, 2012
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In an AC RL/RC circuit, why does phase shift occur?

I understand why there's phase shift when it's only an inductor/capacitor, and why there's no shift when it's only a resistor, but why, if there's both, there can be something like a 30 degree shift.

I see how it fits together mathematically, for the most part, but I don't see how it could possibly satisfy the equation for voltage across an inductor:

e=L*(di/dt)

Anyway, I'm kind of confused, so any help would be appreciated.

2. ### steveb Senior Member

Jul 3, 2008
2,433
469
The voltage across the inductor does obey this relation and the phase shift between the voltage drop on the device and the current through the device is 90 degrees, as you expect.

The voltage in an RL series circuit (across both components) is V=L*(di/dt)+iR. Clearly this is not a simple 90 degree phase shift because the resistor has voltage that is in phase with current.

There is a simple trig identity that allows you to add two sine waves with 90 degree phase difference, as follows.

$A \cos{x}+B \sin{x}=\sqrt{A^2+B^2} \cos({x-\arctan{(B/A)}})$

Now, recall that sine and cosine are 90 degrees differenct in phase, and you can see that the above formula says that something with zero phase shift added to something with 90 degree phase shift, equals a sinusoidal function with a phase that is a mix of the two amplitudes, via the arctangent function.

3. ### russ_hensel Distinguished Member

Jan 11, 2009
821
48
This should give you some incentive to understand differential equations and there solutions, a truly fascinating topic and not just for electronics.