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An inductance L having a resistance R is connected to an alternating source of angular frequency ω. The quality factor (Q) of the inductance is L/R
- a)(ωL/R)2
- b)(R/ωL)1∕2
- c)ωL/R
- d)R/ωL
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
An inductance L having a resistance R is connected to an alternating s...
Ω. The current flowing through the inductance can be represented as:
I = Im sin(ωt + φ)
where Im is the maximum current amplitude and φ is the phase angle.
The voltage across the inductance can be represented as:
V = Vm sin(ωt)
where Vm is the maximum voltage amplitude.
By applying Ohm's law, we can determine the relationship between the voltage and current:
V = IR
Substituting the expressions for V and I:
Vm sin(ωt) = (Im sin(ωt + φ))R
Simplifying the equation:
Vm sin(ωt) = ImR sin(ωt + φ)
Using the trigonometric identity sin(A + B) = sin(A)cos(B) + cos(A)sin(B), we can rewrite the equation as:
Vm sin(ωt) = ImR(sin(ωt)cos(φ) + cos(ωt)sin(φ))
Comparing the coefficients of sin(ωt) and cos(ωt), we get:
Vm = ImRcos(φ)
This equation relates the maximum voltage amplitude (Vm) to the maximum current amplitude (Im), resistance (R), and the phase angle (φ).
I = Im sin(ωt + φ)
where Im is the maximum current amplitude and φ is the phase angle.
The voltage across the inductance can be represented as:
V = Vm sin(ωt)
where Vm is the maximum voltage amplitude.
By applying Ohm's law, we can determine the relationship between the voltage and current:
V = IR
Substituting the expressions for V and I:
Vm sin(ωt) = (Im sin(ωt + φ))R
Simplifying the equation:
Vm sin(ωt) = ImR sin(ωt + φ)
Using the trigonometric identity sin(A + B) = sin(A)cos(B) + cos(A)sin(B), we can rewrite the equation as:
Vm sin(ωt) = ImR(sin(ωt)cos(φ) + cos(ωt)sin(φ))
Comparing the coefficients of sin(ωt) and cos(ωt), we get:
Vm = ImRcos(φ)
This equation relates the maximum voltage amplitude (Vm) to the maximum current amplitude (Im), resistance (R), and the phase angle (φ).
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Community Answer
An inductance L having a resistance R is connected to an alternating s...
Option c
qfacter=Xl/r
= wl /r
qfacter=Xl/r
= wl /r
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An inductance L having a resistance R is connected to an alternating source of angular frequency ω. The quality factor (Q) of the inductance is L/Ra)(ωL/R)2b)(R/ωL)12c)ωL/Rd)R/ωLCorrect answer is option 'C'. Can you explain this answer?
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