A variable frequency 230V alternating source is connected across a series combination of L=5H ,C=80uf and R=40ohm. Calculate (a) the angular frequency of the source which derives the circuit in resonance (b) impedance of the circuit and (c) amplitude of the current at resonance?

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A variable frequency 230V alternating source is connected across a series combination of L=5H ,C=80uf and R=40ohm. Calculate (a) the angular frequency of the source which derives the circuit in resonance (b) impedance of the circuit and (c) amplitude of the current at resonance?

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A variable frequency 230V alternating source is connected across a ser...

Calculating the Angular Frequency:
To find the angular frequency of the source that drives the circuit in resonance, we can use the formula:

Angular frequency (ω) = 1 / √(LC)

Given that L = 5H and C = 80μF, we need to convert the capacitance to Farads by dividing it by 10^6.

C = 80μF / 10^6 = 80 × 10^(-6) F

Now we can substitute the values into the formula:

ω = 1 / √(5 × 80 × 10^(-6))

Simplifying further:

ω = 1 / √(4 ×10^(-3))

Taking the square root of 4 × 10^(-3):

ω = 1 / (0.0632)

Therefore, the angular frequency is approximately 15.82 rad/s.

Calculating the Impedance:
The impedance of the circuit can be calculated using the formula:

Impedance (Z) = √(R^2 + (XL - XC)^2)

Where XL is the inductive reactance and XC is the capacitive reactance.

The inductive reactance can be calculated using the formula:

XL = ωL

Substituting the values:

XL = 15.82 × 5

XL = 79.1 Ω

The capacitive reactance can be calculated using the formula:

XC = 1 / (ωC)

Substituting the values:

XC = 1 / (15.82 × 80 × 10^(-6))

XC = 79.1 Ω

Now we can substitute the values of R, XL, and XC into the impedance formula:

Z = √(40^2 + (79.1 - 79.1)^2)

Simplifying further:

Z = √(1600 + 0)

Z = √1600

Therefore, the impedance of the circuit is 40 Ω.

Calculating the Amplitude of Current at Resonance:
The amplitude of the current at resonance can be calculated using the formula:

Amplitude of Current (I) = Voltage / Impedance

Given that the voltage is 230V, we can substitute the values into the formula:

I = 230 / 40

Simplifying further:

I = 5.75 A

Therefore, the amplitude of the current at resonance is 5.75 Amperes.

Explanation:
- The angular frequency of the source is calculated using the formula 1 / √(LC), where L is the inductance and C is the capacitance of the circuit.
- The impedance of the circuit is calculated using the formula √(R^2 + (XL - XC)^2), where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance.
- The inductive reactance XL is calculated using the formula ωL, where ω is the angular frequency and L is the inductance.
- The capacitive reactance XC is calculated using the formula 1 / (ωC), where ω is the angular frequency and C is the capacitance.
- The amplitude of the current at resonance is calculated using the formula Voltage / Impedance, where

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A variable frequency 230V alternating source is connected across a series combination of L=5H ,C=80uf and R=40ohm. Calculate (a) the angular frequency of the source which derives the circuit in resonance (b) impedance of the circuit and (c) amplitude of the current at resonance? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A variable frequency 230V alternating source is connected across a series combination of L=5H ,C=80uf and R=40ohm. Calculate (a) the angular frequency of the source which derives the circuit in resonance (b) impedance of the circuit and (c) amplitude of the current at resonance? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A variable frequency 230V alternating source is connected across a series combination of L=5H ,C=80uf and R=40ohm. Calculate (a) the angular frequency of the source which derives the circuit in resonance (b) impedance of the circuit and (c) amplitude of the current at resonance?.

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