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A capacitor of capacitance C has reactance X. If capacitance and frequency become double, then the capacitive reactance will be
- a)2X
- b)4X
- c)X/2
- d)X/4
Correct answer is option 'D'. Can you explain this answer?
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A capacitor of capacitance C has reactance X. If capacitance and frequ...
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A capacitor of capacitance C has reactance X. If capacitance and frequ...
Capacitive reactance (Xc) is the opposition offered by a capacitor to the flow of alternating current (AC) due to its capacitance. It is given by the formula:
Xc = 1 / (2πfC)
where Xc is the capacitive reactance, f is the frequency, and C is the capacitance.
If the capacitance (C) and frequency (f) both double, we can analyze the effect on the capacitive reactance as follows:
1. Effect on Capacitance (C):
When the capacitance doubles, it means that the value of C becomes 2C. This indicates that the capacitor can store more charge for a given voltage. However, the reactance of a capacitor is inversely proportional to its capacitance, so the reactance will decrease.
2. Effect on Frequency (f):
When the frequency doubles, it means that the value of f becomes 2f. This indicates that the AC signal is changing at a faster rate. The reactance of a capacitor is inversely proportional to the frequency, so the reactance will also decrease.
3. Calculation of New Capacitive Reactance:
Using the formula for capacitive reactance (Xc = 1 / (2πfC)), we can substitute the new values of C and f to find the new reactance:
New Xc = 1 / (2π(2f)(2C))
= 1 / (4πfC)
= Xc / 4
Therefore, the new capacitive reactance is Xc / 4, which means it becomes one-fourth of its original value.
Hence, the correct answer is option 'D' - X/4.
Xc = 1 / (2πfC)
where Xc is the capacitive reactance, f is the frequency, and C is the capacitance.
If the capacitance (C) and frequency (f) both double, we can analyze the effect on the capacitive reactance as follows:
1. Effect on Capacitance (C):
When the capacitance doubles, it means that the value of C becomes 2C. This indicates that the capacitor can store more charge for a given voltage. However, the reactance of a capacitor is inversely proportional to its capacitance, so the reactance will decrease.
2. Effect on Frequency (f):
When the frequency doubles, it means that the value of f becomes 2f. This indicates that the AC signal is changing at a faster rate. The reactance of a capacitor is inversely proportional to the frequency, so the reactance will also decrease.
3. Calculation of New Capacitive Reactance:
Using the formula for capacitive reactance (Xc = 1 / (2πfC)), we can substitute the new values of C and f to find the new reactance:
New Xc = 1 / (2π(2f)(2C))
= 1 / (4πfC)
= Xc / 4
Therefore, the new capacitive reactance is Xc / 4, which means it becomes one-fourth of its original value.
Hence, the correct answer is option 'D' - X/4.
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