200V A-C is applied at the ends of an LCR circuit- The circuit consists of an inductive reactance XL-50- capacitive reactance XC-50- and ohmic resistance R-10- Calculate the impedance of the circuit and also potential difference across L and R- What will be the potential difference across L-C-

The impedance of L C R circuit is Z=√(( X _ L X _ C ) #160; ^ 2 + R ^ 2 ) =√(( 50 50 ) #160; ^ 2 +( 10 ) #160; ^ 2 ) =10Ω Now the rms current flowi ...

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Byju's Answer

Standard XII

Physics

Magnetic Flux and Faraday's Law

200V A.C is a...

Question

$200 V$ A.C is applied at the ends of an LCR circuit. The circuit consists of an inductive reactance $X_{L} = 50 Ω$ , capacitive reactance $X_{C} = 50 Ω$ and ohmic resistance $R = 10 Ω$ . Calculate the impedance of the circuit and also potential difference across $L$ and $R$ . What will be the potential difference across L-C?

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Solution

The impedance of L-C-R circuit is
$Z = \sqrt{{(X_{L} - X_{C})}^{2} + R^{2}} = \sqrt{{(50 - 50)}^{2} + {(10)}^{2}} = 10 Ω$
Now the rms current flowing in the circuit is
ie $\frac{E}{Z} = \frac{200}{10} = 20 a m p$
The potential difference across the inductance is
$V_{L} = I X_{L} = 20 \times 50 \times = 1000 V, V_{R} = i R = 20 \times 10 = 200 V$
The potential difference across L-C is $(50 - 50) \times 20 = 0$

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200V A.C is applied at the ends of an LCR circuit. The circuit consists of an inductive reactance XL=50Ω, capacitive reactance XC=50Ω and ohmic resistance R=10Ω. Calculate the impedance of the circuit and also potential difference across L and R. What will be the potential difference across L-C?

The impedance of L-C-R circuit isZ=√(XL−XC)2+R2=√(50−50)2+(10)2=10ΩNow the rms current flowing in the circuit isie EZ=20010=20ampThe potential difference across the inductance isVL=IXL=20×50×=1000V,VR=iR=20×10=200VThe potential difference across L-C is (50−50)×20=0