Help me with the ripple current calculations

[explorick]

I wanted to analyse a input capacitor of an LDO on an existing deisgn and confused with the calculations. Please let me know if my calculations are wrong.
The specifications are as follows:
Input cap: 220uF, Max ripple current-0.6A
Input voltage: 12V Batt, Ripple voltage(sinusoidal with 0.5V rms,700 to 13KHz)
The ripple current calculations I did are:
I=V/Z
Z=1/2pi()fC ( Ignoring the impedance of ESR and ESL as they are less)
This equations give me the following values:
Iripple= 0.5*2*pi()*13e3*200e-6 = 8.98A
This value is too high compared to the max ripple rating of capacitor. I think that this output is worng as it is used in existing design.

 

[explorick]

Re: cap-ripple current

The mistake in my calcualtion is ignoring ESR value. The ESR value is 0.86 which cannot be ignored as it is high compared to impedance of cap(0.056ohms). So conisdering ESR the ripple current is 0.575A which is meeting the spec.
Please let me know if this justification is right?