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44. A series LCR circuit driven by 300 V at a
frequency of 50 Hz contains a resistance
R = 3 k2, an inductor of inductive reactance
XL = 250m S and an unknown capacitor. The
value of capacitance to maximize the average
power should be :?
frequency of 50 Hz contains a resistance
R = 3 k2, an inductor of inductive reactance
XL = 250m S and an unknown capacitor. The
value of capacitance to maximize the average
power should be :?
Most Upvoted Answer
44. A series LCR circuit driven by 300 V at afrequency of 50 Hz contai...
Understanding LCR Circuits
In an LCR circuit, the average power is maximized when the circuit is in resonance. Resonance occurs when the inductive reactance (XL) equals the capacitive reactance (XC).
Given Values
- Voltage (V): 300 V
- Frequency (f): 50 Hz
- Resistance (R): 3 kΩ
- Inductive Reactance (XL): 250 mΩ
Resonance Condition
At resonance, the condition can be expressed as:
\[
X_L = X_C
\]
Where:
- \( X_L = 2\pi f L \)
- \( X_C = \frac{1}{2\pi f C} \)
Setting \( X_L \) equal to \( X_C \):
\[
250 \, \Omega = \frac{1}{2\pi (50) C}
\]
Finding Capacitance (C)
Rearranging the equation to solve for C:
\[
C = \frac{1}{2\pi (50)(250)}
\]
Calculating the value:
1. Calculate \( 2\pi (50) \):
- \( 2\pi (50) \approx 314.16 \)
2. Substitute back into the equation:
\[
C = \frac{1}{314.16 \times 250} \approx \frac{1}{78540} \approx 1.27 \times 10^{-5} \, F
\]
Final Result
To maximize the average power, the required capacitance \( C \) is approximately:
\[
C \approx 12.7 \, \mu F
\]
This capacitance ensures the circuit is at resonance, maximizing the average power delivered to the load.
In an LCR circuit, the average power is maximized when the circuit is in resonance. Resonance occurs when the inductive reactance (XL) equals the capacitive reactance (XC).
Given Values
- Voltage (V): 300 V
- Frequency (f): 50 Hz
- Resistance (R): 3 kΩ
- Inductive Reactance (XL): 250 mΩ
Resonance Condition
At resonance, the condition can be expressed as:
\[
X_L = X_C
\]
Where:
- \( X_L = 2\pi f L \)
- \( X_C = \frac{1}{2\pi f C} \)
Setting \( X_L \) equal to \( X_C \):
\[
250 \, \Omega = \frac{1}{2\pi (50) C}
\]
Finding Capacitance (C)
Rearranging the equation to solve for C:
\[
C = \frac{1}{2\pi (50)(250)}
\]
Calculating the value:
1. Calculate \( 2\pi (50) \):
- \( 2\pi (50) \approx 314.16 \)
2. Substitute back into the equation:
\[
C = \frac{1}{314.16 \times 250} \approx \frac{1}{78540} \approx 1.27 \times 10^{-5} \, F
\]
Final Result
To maximize the average power, the required capacitance \( C \) is approximately:
\[
C \approx 12.7 \, \mu F
\]
This capacitance ensures the circuit is at resonance, maximizing the average power delivered to the load.
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44. A series LCR circuit driven by 300 V at afrequency of 50 Hz contains a resistanceR = 3 k2, an inductor of inductive reactanceXL = 250m S and an unknown capacitor. Thevalue of capacitance to maximize the averagepower should be :?
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44. A series LCR circuit driven by 300 V at afrequency of 50 Hz contains a resistanceR = 3 k2, an inductor of inductive reactanceXL = 250m S and an unknown capacitor. Thevalue of capacitance to maximize the averagepower should be :? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 44. A series LCR circuit driven by 300 V at afrequency of 50 Hz contains a resistanceR = 3 k2, an inductor of inductive reactanceXL = 250m S and an unknown capacitor. Thevalue of capacitance to maximize the averagepower should be :? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 44. A series LCR circuit driven by 300 V at afrequency of 50 Hz contains a resistanceR = 3 k2, an inductor of inductive reactanceXL = 250m S and an unknown capacitor. Thevalue of capacitance to maximize the averagepower should be :?.
44. A series LCR circuit driven by 300 V at afrequency of 50 Hz contains a resistanceR = 3 k2, an inductor of inductive reactanceXL = 250m S and an unknown capacitor. Thevalue of capacitance to maximize the averagepower should be :? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 44. A series LCR circuit driven by 300 V at afrequency of 50 Hz contains a resistanceR = 3 k2, an inductor of inductive reactanceXL = 250m S and an unknown capacitor. Thevalue of capacitance to maximize the averagepower should be :? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 44. A series LCR circuit driven by 300 V at afrequency of 50 Hz contains a resistanceR = 3 k2, an inductor of inductive reactanceXL = 250m S and an unknown capacitor. Thevalue of capacitance to maximize the averagepower should be :?.
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