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What does the capacitor do in the ballast circuit?
The capacitor controls the power. Making the ballast more efficient (HPF).
How do you know when the capacitor has gone bad?
The lamp will not normally work if the ballast circuit is a CW or CWA.
Testing is the only way to know when the capacitor has gone bad on HX-HPF and R ballast circuits. On HX-HPF and R the amp draw will almost double when the capacitor fails.