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The reactance offered by a capacitor to alternating current of frequency 50 Hz is 20 Q. If frequency is increased to 100 Hz, reactance becomes_____ohms.
- a)2.5
- b)5
- c)10
- d)15
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The reactance offered by a capacitor to alternating current of frequen...
Capacitive reactance
Xc = 1/2πf
Therefore XC1/XC2 = 2πf2/2πf1
= 20/XC2 =100/50
= XC2 = 10
Most Upvoted Answer
The reactance offered by a capacitor to alternating current of frequen...
Given:
Frequency, f1 = 50 Hz
Reactance, X1 = 20 Ω
Frequency, f2 = 100 Hz
To find: Reactance, X2 at frequency f2
Formula used:
Reactance of a capacitor, X = 1/(2πfC)
where,
f = frequency
C = capacitance
Explanation:
The reactance of a capacitor is inversely proportional to the frequency of the applied AC voltage. As the frequency of the AC voltage increases, the reactance of the capacitor decreases.
Using the formula, we can find the capacitance of the capacitor at frequency f1.
X1 = 1/(2πf1C)
C = 1/(2πf1X1) = 1/(2π×50×20) = 1/(6280) = 0.000159 F
Now, we can find the reactance of the same capacitor at frequency f2.
X2 = 1/(2πf2C) = 1/(2π×100×0.000159) = 10 Ω
Therefore, the reactance of the capacitor at frequency 100 Hz is 10 Ω.
Answer: Option (c) 10 Ω.
Frequency, f1 = 50 Hz
Reactance, X1 = 20 Ω
Frequency, f2 = 100 Hz
To find: Reactance, X2 at frequency f2
Formula used:
Reactance of a capacitor, X = 1/(2πfC)
where,
f = frequency
C = capacitance
Explanation:
The reactance of a capacitor is inversely proportional to the frequency of the applied AC voltage. As the frequency of the AC voltage increases, the reactance of the capacitor decreases.
Using the formula, we can find the capacitance of the capacitor at frequency f1.
X1 = 1/(2πf1C)
C = 1/(2πf1X1) = 1/(2π×50×20) = 1/(6280) = 0.000159 F
Now, we can find the reactance of the same capacitor at frequency f2.
X2 = 1/(2πf2C) = 1/(2π×100×0.000159) = 10 Ω
Therefore, the reactance of the capacitor at frequency 100 Hz is 10 Ω.
Answer: Option (c) 10 Ω.
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