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The series arm impedance of a filter consists of a 0.5 micro farad capacitor in series
with an inductor of 0.35 H. If R0 = 500 ohms, determine the elements in the shunt
arm and the manner in which they may be connected. Find the frequency of
resonance f0.?
with an inductor of 0.35 H. If R0 = 500 ohms, determine the elements in the shunt
arm and the manner in which they may be connected. Find the frequency of
resonance f0.?
Most Upvoted Answer
The series arm impedance of a filter consists of a 0.5 micro farad cap...
Introduction:
In this problem, we are given the series arm impedance of a filter consisting of a capacitor and an inductor. We are also given the value of R0 and we have to determine the elements in the shunt arm and the frequency of resonance.
Calculation of Shunt Arm:
The shunt arm of a filter is connected in parallel to the series arm. The shunt arm consists of a resistor and a capacitor. The value of the resistor can be determined using the formula:
R = R0 * (1 + Q^2)
where Q is the quality factor of the circuit. The quality factor can be calculated using the formula:
Q = 1 / R * sqrt(L / C)
where L is the inductance of the series arm and C is the capacitance of the series arm.
Substituting the given values, we get:
Q = 1 / 500 * sqrt(0.35 / 0.5 * 10^-6) = 148.92
R = 500 * (1 + 148.92^2) = 1.11 * 10^8 ohms
The value of the shunt arm resistor is 1.11 * 10^8 ohms.
The value of the shunt arm capacitor can be calculated using the formula:
C = 1 / (R * f0^2 * L)
where f0 is the frequency of resonance.
Substituting the given values, we get:
C = 1 / (1.11 * 10^8 * f0^2 * 0.35) = 4.03 * 10^-15 farads
The value of the shunt arm capacitor is 4.03 * 10^-15 farads.
Calculation of Frequency of Resonance:
The frequency of resonance can be calculated using the formula:
f0 = 1 / (2 * pi * sqrt(L * C))
Substituting the given values, we get:
f0 = 1 / (2 * pi * sqrt(0.35 * 0.5 * 10^-6 * 4.03 * 10^-15)) = 1.77 MHz
The frequency of resonance is 1.77 MHz.
Explanation:
In this problem, we have calculated the shunt arm elements and the frequency of resonance of a filter. The shunt arm consists of a resistor and a capacitor connected in parallel to the series arm. The value of the shunt arm resistor is calculated using the formula R = R0 * (1 + Q^2), where Q is the quality factor of the circuit. The value of the shunt arm capacitor is calculated using the formula C = 1 / (R * f0^2 * L). The frequency of resonance is calculated using the formula f0 = 1 / (2 * pi * sqrt(L * C)). The frequency of resonance is the frequency at which the filter has maximum attenuation. In this problem, the frequency of resonance is 1.77 MHz.
In this problem, we are given the series arm impedance of a filter consisting of a capacitor and an inductor. We are also given the value of R0 and we have to determine the elements in the shunt arm and the frequency of resonance.
Calculation of Shunt Arm:
The shunt arm of a filter is connected in parallel to the series arm. The shunt arm consists of a resistor and a capacitor. The value of the resistor can be determined using the formula:
R = R0 * (1 + Q^2)
where Q is the quality factor of the circuit. The quality factor can be calculated using the formula:
Q = 1 / R * sqrt(L / C)
where L is the inductance of the series arm and C is the capacitance of the series arm.
Substituting the given values, we get:
Q = 1 / 500 * sqrt(0.35 / 0.5 * 10^-6) = 148.92
R = 500 * (1 + 148.92^2) = 1.11 * 10^8 ohms
The value of the shunt arm resistor is 1.11 * 10^8 ohms.
The value of the shunt arm capacitor can be calculated using the formula:
C = 1 / (R * f0^2 * L)
where f0 is the frequency of resonance.
Substituting the given values, we get:
C = 1 / (1.11 * 10^8 * f0^2 * 0.35) = 4.03 * 10^-15 farads
The value of the shunt arm capacitor is 4.03 * 10^-15 farads.
Calculation of Frequency of Resonance:
The frequency of resonance can be calculated using the formula:
f0 = 1 / (2 * pi * sqrt(L * C))
Substituting the given values, we get:
f0 = 1 / (2 * pi * sqrt(0.35 * 0.5 * 10^-6 * 4.03 * 10^-15)) = 1.77 MHz
The frequency of resonance is 1.77 MHz.
Explanation:
In this problem, we have calculated the shunt arm elements and the frequency of resonance of a filter. The shunt arm consists of a resistor and a capacitor connected in parallel to the series arm. The value of the shunt arm resistor is calculated using the formula R = R0 * (1 + Q^2), where Q is the quality factor of the circuit. The value of the shunt arm capacitor is calculated using the formula C = 1 / (R * f0^2 * L). The frequency of resonance is calculated using the formula f0 = 1 / (2 * pi * sqrt(L * C)). The frequency of resonance is the frequency at which the filter has maximum attenuation. In this problem, the frequency of resonance is 1.77 MHz.
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The series arm impedance of a filter consists of a 0.5 micro farad capacitor in serieswith an inductor of 0.35 H. If R0 = 500 ohms, determine the elements in the shuntarm and the manner in which they may be connected. Find the frequency ofresonance f0.?
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The series arm impedance of a filter consists of a 0.5 micro farad capacitor in serieswith an inductor of 0.35 H. If R0 = 500 ohms, determine the elements in the shuntarm and the manner in which they may be connected. Find the frequency ofresonance f0.? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about The series arm impedance of a filter consists of a 0.5 micro farad capacitor in serieswith an inductor of 0.35 H. If R0 = 500 ohms, determine the elements in the shuntarm and the manner in which they may be connected. Find the frequency ofresonance f0.? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The series arm impedance of a filter consists of a 0.5 micro farad capacitor in serieswith an inductor of 0.35 H. If R0 = 500 ohms, determine the elements in the shuntarm and the manner in which they may be connected. Find the frequency ofresonance f0.?.
The series arm impedance of a filter consists of a 0.5 micro farad capacitor in serieswith an inductor of 0.35 H. If R0 = 500 ohms, determine the elements in the shuntarm and the manner in which they may be connected. Find the frequency ofresonance f0.? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about The series arm impedance of a filter consists of a 0.5 micro farad capacitor in serieswith an inductor of 0.35 H. If R0 = 500 ohms, determine the elements in the shuntarm and the manner in which they may be connected. Find the frequency ofresonance f0.? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The series arm impedance of a filter consists of a 0.5 micro farad capacitor in serieswith an inductor of 0.35 H. If R0 = 500 ohms, determine the elements in the shuntarm and the manner in which they may be connected. Find the frequency ofresonance f0.?.
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