Verification of the capacitance of a capacitor

In summary, to verify the capacitance of the conductor in the given circuit, the phase difference between the current and voltage can be adjusted to 15 degrees by increasing the capacitance. This is because the greater the capacitance, the smaller the capacitive reactance, resulting in a smaller phase difference between the current and voltage.
  • #1
Samar A
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Homework Statement


In the circuit shown in the figure below, the hase difference between the current and the voltage is 30 degrees, show how could you verify the capacitance of the conductor so that the phase difference could be 15 degrees.
Muz9U.jpg

Homework Equations


tan θ=-Xc/R (the phase difference in the RC cirucit with an AC source)

The Attempt at a Solution


That is my attempt, I show how much would be the value of the capacitance in the second case mathematically.
2VX1D.png

Is it correct?
 
Last edited:
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  • #2
Samar A said:
show how could you verify the conductance **capacitance** of the conductor so that the phase difference could be 15 degrees.
Conductance is the reciprocal of resistance. What you have in the circuit is a capacitor (or condenser).
I didn't check your actual values step by step, but your approach is correct. Also, the new capacitance is coming out to be more than the old capacitance, which is correct (can you think why?).
 
  • #3
cnh1995 said:
Conductance is the reciprocal of resistance. What you have in the circuit is a capacitor (or condenser).
Oh, sorry, I corrected it.
cnh1995 said:
can you think why?).
OK, I think because when the capacitance is greater the reactance of the capacitor will be less than the original one, so its effect in the circuit will be smaller, and then the phase difference between the current and the voltage will be smaller too. Am I right?
 
  • #4
Samar A said:
OK, I think because when the capacitance is greater the inductance **reactance** of the capacitor will be less than the original one, so its effect in the circuit will be smaller, and then the phase difference between the current and the voltage will be smaller too. Am I right?
Right. Capacitive reactance is inversely proportional to the capacitance.
 
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1. What is capacitance and how is it measured?

Capacitance is the ability of a capacitor to store electric charge. It is measured in units of Farads (F) and is typically denoted by the symbol "C". The capacitance of a capacitor can be measured using an instrument called a capacitance meter or by using the formula C = Q/V, where Q is the charge stored in the capacitor and V is the voltage across the capacitor.

2. What is the importance of verifying the capacitance of a capacitor?

Verifying the capacitance of a capacitor is important because it ensures that the capacitor is functioning correctly and is able to store the desired amount of charge. It also allows for the proper selection and use of capacitors in electronic circuits.

3. How can the capacitance of a capacitor be verified?

The capacitance of a capacitor can be verified using a capacitance meter, which measures the capacitance directly, or by using an oscilloscope and a known AC voltage source to measure the capacitive reactance, which can then be used to calculate the capacitance. Another method is to use a time constant circuit with a known resistance and measure the time it takes for the capacitor to charge to a certain voltage, which can then be used to calculate the capacitance.

4. Can the capacitance of a capacitor change over time?

Yes, the capacitance of a capacitor can change over time due to factors such as aging and environmental conditions. This is why it is important to regularly verify the capacitance of capacitors in electronic circuits.

5. What are some common errors when measuring the capacitance of a capacitor?

Some common errors when measuring the capacitance of a capacitor include using the wrong unit of measurement, using a damaged or malfunctioning capacitance meter, and not taking into account the stray capacitance of the circuit being measured. It is important to carefully follow the instructions of the measuring instrument and consider any potential sources of error.

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