An AC generator producing 10V(rms) at 200 rad/s is connected in series with a $50 \Omega$ resistor, a 400 mH inductor and a $200 \mu F$ capacitor. The rms voltage across the inductor is
- 2.5 V
- 3.4 V
- 6.7 V
- 10.8 V
The Correct Option is D
Solution and Explanation
$\omega =200 \,rad / s $
$R =50 \,\Omega$
$L =400 \,mH $
$C =200 \,\mu F$
We know that,
$Z=\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}}$
$=\sqrt{(50)^{2}+(80-25)^{2}}=\sqrt{(50)^{2}-(55)^{2}} $
$=\sqrt{2500+3025} $
$Z =\sqrt{5525}=74.3 \,\Omega $
$I =\frac{E}{Z}=\frac{10}{74.3}=0.13459 A$
$E_{L} =I X_{L}=0.13459 \times 80 $
$=10.76 V \text { or } 10.8 V $
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Concepts Used:
LCR Circuit
An LCR circuit, also known as a resonant circuit, or an RLC circuit, is an electrical circuit consist of an inductor (L), capacitor (C) and resistor (R) connected in series or parallel.
Series LCR circuit
When a constant voltage source is connected across a resistor a current is induced in it. This current has a unique direction and flows from the negative to positive terminal. Magnitude of current remains constant.
Alternating current is the current if the direction of current through this resistor changes periodically. An AC generator or AC dynamo can be used as AC voltage source.
