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E=I x R. The inductive spike occurs as the circuit is opened. The collapsing magnetic field causes the inductor to become the source of the circuit. For example consider a circuit consisting of a 10 volt battery, a 10 mh inductor, and a 10 ohm resistor all in series. With the switch closed, 1 amp will flow through the circuit (after 5 mS). The 5 mS is the time it takes the current to rise from 0 to 1 amp. This is given by the formual TC=L/R where TC is the time constant in seconds, L is the inductance in henries, and R is the resistance in ohms. It takes 5 time constants for the current to reach the maximum current which is determined by I=E/R (Ohm's Law). The delay is caused by the counter EMF generated in the coil as flux lines cut through adjacent turns of the inductor. After 5 time constants, the current is at 1 amp. When we open the switch, it will take 5 time constants for the current to drop to 0 amps. However, this will not be 5 mS because the resistance is now much larger do to the opening switch contacts. The voltage across the switch contacts will be whatever is necessary to maintain the current flow for the 5 time constants. After one time constant, the current will have dropped to 32% of the maximum current or in this case, 0.32 amps. If the resistance of the switch gap is 1 megohm, the the voltage will be 320,000 volts. More than enough to ionize the air and create a conductive path. If we assume an average resistance of 1 megohm, it will take 50 nS for the current to drop to 0. Of course during this time, the switch contact gets zapped. Placing a diode across the inductor such that the diode is reverse biased with the switch closed will give the current an alternate path as the polarity of the inductor reverses when the magnetic field collapses and the inductor becomes the source. This lowers the voltage from 1,000,000 volts to 0.7 volts. The downside is that the time it takes for the current decrease increases bo the ratio of 1,000,000/0.7. In a relay, this may cause the relay to "chatter" when opening. Adding a zener diode in series anode to anode with the spike suppressing diode will alleivate most chattering problems. A 34.3 volt zener will raise the voltage from 0,7v to 35v and shorten the time by a factor of 50 (35/.0.7).

Q: What is the formula for transient spike computation in an inductive load?

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When you close an inductive circuit, since an inductor resists a change in current, the initial reaction of the load is to look like a high resistance. As current builds, the resistance falls. With a theoretical source and inductor, current would eventually reach infinity, that is after infinite time, but practical sources and inductors will reach a plateau current. When you open an inductive circuit, again, since an inductor resists a change in current, the inductor attempts to maintain that current, but there is no conductivity for that current so, the inductor presents a high voltage spike in the reverse direction it was initially "charged" with. With a theoretical inductor, and theoretical infinite impedance, the voltage spike would be infinite. Again, practical inductors have a maximum voltage spike, but this spike can still be quite high, even thousands of volts, which can damage the circuit, so it is important to maintain a conduction path for the collapsing field, often a diode, or a resistor/capacitor filter.

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When you close an inductive circuit, since an inductor resists a change in current, the initial reaction of the load is to look like a high resistance. As current builds, the resistance falls. With a theoretical source and inductor, current would eventually reach infinity, that is after infinite time, but practical sources and inductors will reach a plateau current. When you open an inductive circuit, again, since an inductor resists a change in current, the inductor attempts to maintain that current, but there is no conductivity for that current so, the inductor presents a high voltage spike in the reverse direction it was initially "charged" with. With a theoretical inductor, and theoretical infinite impedance, the voltage spike would be infinite. Again, practical inductors have a maximum voltage spike, but this spike can still be quite high, even thousands of volts, which can damage the circuit, so it is important to maintain a conduction path for the collapsing field, often a diode, or a resistor/capacitor filter.

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