# Solved: Leaky Capacitor Problem with Zc=74.5 Ohm

• suryakalpo
In summary, the problem involves a series circuit with a leaky capacitor, coil, and resistor. The goal is to find the loss in the capacitor. The impedance equation was used to calculate the values for the coil and the entire circuit, but an incorrect calculation led to an imaginary value for the leakage resistance. The correct approach would be to represent the leakage with a parallel resistor and use parallel impedance calculations.
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

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

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.

## 1. What is a leaky capacitor?

A leaky capacitor is a type of capacitor that has a higher than normal leakage current, meaning it allows more current to flow through it than it should. This can lead to problems with the performance of the capacitor and the circuit it is a part of.

## 2. How does a leaky capacitor affect a circuit?

A leaky capacitor can cause a variety of issues in a circuit, including decreased efficiency, increased power consumption, and distorted signals. It can also cause the circuit to malfunction or fail completely.

## 3. What causes a capacitor to become leaky?

There are several factors that can contribute to a capacitor becoming leaky, including overvoltage, high temperatures, and physical damage. In some cases, it may also be due to a manufacturing defect.

## 4. How can a leaky capacitor problem be solved?

The best way to solve a leaky capacitor problem is to replace the faulty capacitor with a new one. It is important to ensure that the replacement capacitor has the correct specifications, including the correct capacitance and voltage rating.

## 5. How can I prevent a capacitor from becoming leaky?

To prevent a capacitor from becoming leaky, it is important to select capacitors with the proper specifications for the circuit they will be used in. It is also important to operate the capacitor within its rated voltage and temperature limits. Regular maintenance and testing can also help detect and prevent leaky capacitors.

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