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36. A100 Sresistance, a0.1uFcapacitor and
an inductor are connected inseries across a
250 V supply at variable frequency. Calculate
the value of inductance of inductor at which
resonance will occur. Given that the resonant
frequency is 60 HZ. JEE (Main)-2021]?
an inductor are connected inseries across a
250 V supply at variable frequency. Calculate
the value of inductance of inductor at which
resonance will occur. Given that the resonant
frequency is 60 HZ. JEE (Main)-2021]?
Most Upvoted Answer
36. A100 Sresistance, a0.1uFcapacitor andan inductor are connected ins...
To calculate the value of inductance at which resonance occurs in an RLC series circuit, we need to understand the resonance condition.
Resonance Condition
At resonance, the inductive reactance (XL) equals the capacitive reactance (XC). The formulas for these reactances are:
- Inductive Reactance:
XL = 2πfL
where f is the frequency and L is the inductance.
- Capacitive Reactance:
XC = 1/(2πfC)
where C is the capacitance.
Given Values
- Resonant Frequency (f) = 60 Hz
- Capacitance (C) = 0.1 μF = 0.1 × 10^-6 F
- Resistance (R) = 36 Ω (not directly needed for resonance calculation)
Setting Up the Equation
At resonance:
XL = XC
This implies:
2πfL = 1/(2πfC)
Rearranging for L
To find L, we can rearrange the equation:
L = 1/(4π²f²C)
Substituting Values
Now substitute the values of f and C:
L = 1/(4π²(60)²(0.1 × 10^-6))
Calculating:
- First, calculate 4π²(60)²:
4π²(60)² ≈ 4 × 9.87 × 3600 ≈ 141372.6
- Now calculate L:
L ≈ 1/(141372.6 × 0.1 × 10^-6) ≈ 1/(0.01413726) ≈ 70.7 H
Final Result
Thus, the value of inductance L at which resonance occurs is approximately 70.7 H.
Resonance Condition
At resonance, the inductive reactance (XL) equals the capacitive reactance (XC). The formulas for these reactances are:
- Inductive Reactance:
XL = 2πfL
where f is the frequency and L is the inductance.
- Capacitive Reactance:
XC = 1/(2πfC)
where C is the capacitance.
Given Values
- Resonant Frequency (f) = 60 Hz
- Capacitance (C) = 0.1 μF = 0.1 × 10^-6 F
- Resistance (R) = 36 Ω (not directly needed for resonance calculation)
Setting Up the Equation
At resonance:
XL = XC
This implies:
2πfL = 1/(2πfC)
Rearranging for L
To find L, we can rearrange the equation:
L = 1/(4π²f²C)
Substituting Values
Now substitute the values of f and C:
L = 1/(4π²(60)²(0.1 × 10^-6))
Calculating:
- First, calculate 4π²(60)²:
4π²(60)² ≈ 4 × 9.87 × 3600 ≈ 141372.6
- Now calculate L:
L ≈ 1/(141372.6 × 0.1 × 10^-6) ≈ 1/(0.01413726) ≈ 70.7 H
Final Result
Thus, the value of inductance L at which resonance occurs is approximately 70.7 H.
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36. A100 Sresistance, a0.1uFcapacitor andan inductor are connected inseries across a250 V supply at variable frequency. Calculatethe value of inductance of inductor at whichresonance will occur. Given that the resonantfrequency is 60 HZ. JEE (Main)-2021]?
Question Description
36. A100 Sresistance, a0.1uFcapacitor andan inductor are connected inseries across a250 V supply at variable frequency. Calculatethe value of inductance of inductor at whichresonance will occur. Given that the resonantfrequency is 60 HZ. JEE (Main)-2021]? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 36. A100 Sresistance, a0.1uFcapacitor andan inductor are connected inseries across a250 V supply at variable frequency. Calculatethe value of inductance of inductor at whichresonance will occur. Given that the resonantfrequency is 60 HZ. JEE (Main)-2021]? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 36. A100 Sresistance, a0.1uFcapacitor andan inductor are connected inseries across a250 V supply at variable frequency. Calculatethe value of inductance of inductor at whichresonance will occur. Given that the resonantfrequency is 60 HZ. JEE (Main)-2021]?.
36. A100 Sresistance, a0.1uFcapacitor andan inductor are connected inseries across a250 V supply at variable frequency. Calculatethe value of inductance of inductor at whichresonance will occur. Given that the resonantfrequency is 60 HZ. JEE (Main)-2021]? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 36. A100 Sresistance, a0.1uFcapacitor andan inductor are connected inseries across a250 V supply at variable frequency. Calculatethe value of inductance of inductor at whichresonance will occur. Given that the resonantfrequency is 60 HZ. JEE (Main)-2021]? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 36. A100 Sresistance, a0.1uFcapacitor andan inductor are connected inseries across a250 V supply at variable frequency. Calculatethe value of inductance of inductor at whichresonance will occur. Given that the resonantfrequency is 60 HZ. JEE (Main)-2021]?.
Solutions for 36. A100 Sresistance, a0.1uFcapacitor andan inductor are connected inseries across a250 V supply at variable frequency. Calculatethe value of inductance of inductor at whichresonance will occur. Given that the resonantfrequency is 60 HZ. JEE (Main)-2021]? in English & in Hindi are available as part of our courses for UPSC.
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