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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 'C'. Can you explain this answer?
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Option C....because Xc is inversely proportional to frequency....if f increases Xc decreases....
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The reactance offered by a capacitor to alternating current of frequen...
Given:
- Frequency of alternating current (AC) = 50 Hz
- Reactance of the capacitor at 50 Hz = 20 Q
To find:
- Reactance of the capacitor at 100 Hz
Solution:
1. Understanding Reactance
Reactance is the opposition offered by a component (in this case, a capacitor) to the flow of alternating current. It is measured in ohms (Ω). The reactance of a capacitor depends on the frequency of the AC signal.
2. Capacitive Reactance Formula
The reactance (Xc) of a capacitor is given by the formula:
Xc = 1 / (2πfC)
where:
Xc = Capacitive reactance in ohms (Ω)
f = Frequency of the AC signal in hertz (Hz)
C = Capacitance of the capacitor in farads (F)
3. Calculating Reactance at 50 Hz
Given that the reactance at 50 Hz is 20 Q, we can rearrange the formula to solve for capacitance:
20 = 1 / (2π * 50 * C)
C = 1 / (2π * 50 * 20)
C ≈ 1 / 628.32
C ≈ 0.00159 F
4. Calculating Reactance at 100 Hz
Now, we need to calculate the reactance at 100 Hz using the same capacitor. Substituting the new frequency into the formula:
Xc = 1 / (2π * 100 * 0.00159)
Xc ≈ 1 / 0.318
Xc ≈ 3.14 Ω
5. Answer
Therefore, the reactance of the capacitor at 100 Hz is approximately 3.14 Ω.
None of the given options match the calculated value. There seems to be an error in the options provided.
- Frequency of alternating current (AC) = 50 Hz
- Reactance of the capacitor at 50 Hz = 20 Q
To find:
- Reactance of the capacitor at 100 Hz
Solution:
1. Understanding Reactance
Reactance is the opposition offered by a component (in this case, a capacitor) to the flow of alternating current. It is measured in ohms (Ω). The reactance of a capacitor depends on the frequency of the AC signal.
2. Capacitive Reactance Formula
The reactance (Xc) of a capacitor is given by the formula:
Xc = 1 / (2πfC)
where:
Xc = Capacitive reactance in ohms (Ω)
f = Frequency of the AC signal in hertz (Hz)
C = Capacitance of the capacitor in farads (F)
3. Calculating Reactance at 50 Hz
Given that the reactance at 50 Hz is 20 Q, we can rearrange the formula to solve for capacitance:
20 = 1 / (2π * 50 * C)
C = 1 / (2π * 50 * 20)
C ≈ 1 / 628.32
C ≈ 0.00159 F
4. Calculating Reactance at 100 Hz
Now, we need to calculate the reactance at 100 Hz using the same capacitor. Substituting the new frequency into the formula:
Xc = 1 / (2π * 100 * 0.00159)
Xc ≈ 1 / 0.318
Xc ≈ 3.14 Ω
5. Answer
Therefore, the reactance of the capacitor at 100 Hz is approximately 3.14 Ω.
None of the given options match the calculated value. There seems to be an error in the options provided.
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