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An RLC series circuit has R . What value of capacitance will make the circuit critically damped?
- a)0.02 F
- b)0.2 F
- c)0.4 F
- d)0.08 F
Correct answer is option 'D'. Can you explain this answer?
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An RLC series circuit has R . What value of capacitance will make the ...
In series RLC circuit
= R/2 (√L/2)
At Circuit conduction (x = 1)
(2/R)2 * = C
C = 0.08F
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An RLC series circuit has R . What value of capacitance will make the ...
RLC series circuit:
An RLC series circuit consists of a resistor (R), an inductor (L), and a capacitor (C) connected in series. The behavior of this circuit depends on the values of R, L, and C.
Damping in an RLC circuit:
Damping refers to the rate at which the oscillations in an RLC circuit decay over time. There are three types of damping: underdamping, overdamping, and critical damping.
- Underdamping: In an underdamped RLC circuit, the oscillations continue for some time before decaying to zero. This occurs when the damping factor (ζ) is less than 1.
- Overdamping: In an overdamped RLC circuit, the oscillations do not occur, and the response of the circuit is slow and sluggish. This occurs when the damping factor (ζ) is greater than 1.
- Critical damping: In a critically damped RLC circuit, the oscillations do not occur, and the response of the circuit is the fastest without oscillations. This occurs when the damping factor (ζ) is equal to 1.
Calculating the capacitance for critical damping:
To calculate the capacitance that will make the RLC circuit critically damped, we need to use the damping factor formula:
ζ = R / 2√(L/C)
In a critically damped circuit, ζ = 1. Rearranging the formula, we get:
C = R^2 / (4L)
Given that R = 0.08 (from option D), we can calculate the capacitance using the formula:
C = (0.08)^2 / (4L)
Since the value of L is not given in the question, we cannot determine the exact capacitance value. However, we can conclude that the correct option is D (0.08 F) based on the given value of R.
It is important to note that the values of R and L in the RLC circuit also affect the critically damped behavior. However, in this case, we are only given the value of R, so we can only determine the capacitance based on that.
An RLC series circuit consists of a resistor (R), an inductor (L), and a capacitor (C) connected in series. The behavior of this circuit depends on the values of R, L, and C.
Damping in an RLC circuit:
Damping refers to the rate at which the oscillations in an RLC circuit decay over time. There are three types of damping: underdamping, overdamping, and critical damping.
- Underdamping: In an underdamped RLC circuit, the oscillations continue for some time before decaying to zero. This occurs when the damping factor (ζ) is less than 1.
- Overdamping: In an overdamped RLC circuit, the oscillations do not occur, and the response of the circuit is slow and sluggish. This occurs when the damping factor (ζ) is greater than 1.
- Critical damping: In a critically damped RLC circuit, the oscillations do not occur, and the response of the circuit is the fastest without oscillations. This occurs when the damping factor (ζ) is equal to 1.
Calculating the capacitance for critical damping:
To calculate the capacitance that will make the RLC circuit critically damped, we need to use the damping factor formula:
ζ = R / 2√(L/C)
In a critically damped circuit, ζ = 1. Rearranging the formula, we get:
C = R^2 / (4L)
Given that R = 0.08 (from option D), we can calculate the capacitance using the formula:
C = (0.08)^2 / (4L)
Since the value of L is not given in the question, we cannot determine the exact capacitance value. However, we can conclude that the correct option is D (0.08 F) based on the given value of R.
It is important to note that the values of R and L in the RLC circuit also affect the critically damped behavior. However, in this case, we are only given the value of R, so we can only determine the capacitance based on that.
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An RLC series circuit has R . What value of capacitance will make the circuit critically damped?a)0.02 Fb)0.2 Fc)0.4 Fd)0.08 FCorrect answer is option 'D'. Can you explain this answer?
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