Solved: Leaky Capacitor Problem with Zc=74.5 Ohm

[suryakalpo]

1. The problem statement:

A leaky capacitor, Zc =74.5 ohm is in series with a coil Z coil = 40 ohm and a resistor R=50 ohm. When a voltage V=200V is applied I=2.5A and the p.d across R and Z coil is combined is 194V. Find the loss in the capacitor.

Homework Equations

Z=(R^2 + (XL - XC)^2)^0.5

The Attempt at a Solution

I have used the impedence eqn for the coil and obtained the inductance and resistance of the coil as r=19.22 ohm and XL = 35.08 ohm

Then I applied the impedence eqn to the entire ckt and obtained the value of Xc = 75.19 ohm.

Now, a leaky capacitor can be represented by a non-leaky capacitor in parallel with a resistance (i hope its right!). But on equating both these capacitive impedences I'm getting an imaginary value of resistance.

I can't figure out where exactly have i gone wrong...if its the theory of the leaky capacitor or mi calculations..please suggest something

 

[suryakalpo]

guys if u need more clarification abt the question please let me know

 

[Adjuster]

A parallel resistor is a valid way to represent capacitor leakage, but if you represent leakage this way, you don't calculate it in the same way as a series impedance.

I have not checked your value of 75.19ohm for Xc, but one would expect it to be greater than the total capacitor impedance, in this case 74.5 ohm. Correct application of parallel impedance maths should indeed yield a real positive value for the leakage resistance.

Good luck.