.Why would I need to use the ballast resistor if using an e coil similar to what vehicles that came from factory with a TFI module used?
As I said, it depends on the Coil used,
and,
the way that the particular Ignition-Module or ECU used handles Coil "Dwell-Time".
One of the pictures You provided shows a Coil that is integrated into the Distributor,
if You intend to re-use that Coil, You must know how it was designed to be used, ( with a Ballast-Resistor )..
A Ballast-Resistor is designed to limit the Power going to the Coil during periods where
the Dwell-Time may be inadvertently "excessive",
such as when the Ignition-Key is "On", but the Engine is not running,
or the Points are severely out of adjustment, causing excessive Dwell-Time,
either of which can cause the Coil to overheat and fail.
The Ballast-Resistor is taken out of Circuit during Starter-Engagement because the Starter will
most definitely cause the Battery-Voltage to drop, which can cause a very weak-Spark, or no Spark at all.
Cranking periods are normally not long enough to cause the Coil to build-up excessive Heat.
Most automotive ECUs Electronically control the Coil-Dwell-Time,
based on Voltage, Temperature, Cranking, Engine-Load, Engine-RPM,
and a variety of other monitored factors.
But, a Points-style Ignition-System has no control over Dwell-Time,
therefore, it must be designed for "worst-case" conditions.
Only the Points-Gap, and RPM, will change the Dwell-Time, in a Points-style Ignition-System,
and the Dwell-change vs RPM is practically the reverse of what would be the most ideal.
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