# 24VAC vs 220VAC inductive voltage transient

I'm designing a PCB with a PIC micro-controller that has to switch some contactors. This PIC drives some NPN BJT transistors and these transistors drive some Relays that switch the contactors.

I'm trying to minimize EMI interference and sparks in my circuit and for thus i have to decide what coils to use on the contactors (and snubbers but thats not related to the question).

Seaching for contactors I've got two models (for the coil):

1) 7VA, cos(phi)=0.3 (50Hz), 24VAC.

2) 7VA, cos(phi)=0.3 (50Hz), 220VAC.

What's the comparison between both voltage spikes when the coil is suddenly opened ? (How much higher, how much longer, frequency, etc)

7 VA at 24 V AC means a current of 7/24 amps or 292 mA. From this, the impedance is 24/0.292 = 82.3 ohms. From the cos(phi) bit you can then calculate the series inductive reactance and resistance that add up to the 82.3 ohms.

So, assuming you can do this (I get XL = 78.5 ohms), convert this to inductance and you have everything needed to compute the stored energy ($\dfrac{I^2L}{2}$).

Compare the energy in both scenarios and the one with the highest energy storage capability is the one that could generate the bigger spark.

What's the comparison between both voltage spikes when the coil is suddenly opened ? (How much higher, how much longer, frequency, etc)

Higher and longer is about energy and control of that discharge of energy. Frequency is much harder to predict because you haven't stated what the parasitic components (or sunubber) are.

• Thanks, just one question, when calculating the Energy is $I^2 = |I|^2$ ? or is $I$ the real part of the current ? – Tomás Arturo Herrera Castro May 14 '17 at 17:31
• As far as pure inductor is concerned, there is no real or imaginary current so, any current flowing in the inductor at any moment in time represents stored energy. – Andy aka May 14 '17 at 17:52
• So, you will liberate the most energy when the current is maximimum or, for an inductor fed from a sinewave, when voltage passes through 0 volts. – Andy aka May 14 '17 at 17:54
• No need for thanks. The normal thing is to up-vote an answer or, in your case (the guy making the question), to formally accept the answer. – Andy aka May 15 '17 at 7:13