In a series resonant LCR circuit, the voltage across R is 100V and R=1kΩ with C=2μF . The resonant frequency ω is 200rads- 1 . At resonance the voltage across textitL is

Question

In a series resonant LCR circuit, the voltage across R is 100V and R=1kΩ with C=2μF . The resonant frequency ω is 200rads- 1 . At resonance the voltage across textitL is (A) 4× 10- 3V (B) 2.5× 10- 2V (C) 40V (D) 250V

Tardigrade Admin · Accepted Answer

Current, I=(E/Z) where, E=√VR2 + (VL - VC)2 Z=√R2 + (XL - XC)2 At resonance, XL=XC ∴ Z=R Again at resonance, VL=VC ∴ E=VR ∴ I=(VR/R)=(100/1 × 103)= 0.1A ∴ VL=I L ω=(I/C ω)=(0.1/(2 × 10-6) ×(200)) ∴ VL=250V .

Q. In a series resonant $L CR$ circuit, the voltage across $R$ is $100 V$ and $R = 1 k Ω$ with $C = 2 μ F$ . The resonant frequency $ω$ is $200 r a d s^{- 1}$ . At resonance the voltage across $L$ is

$4 \times 1 0^{- 3} V$

$2.5 \times 1 0^{- 2} V$

$40 V$

$250 V$

Q. In a series resonant LCR circuit, the voltage across R is 100V and R=1kΩ with C=2μF . The resonant frequency ω is 200rads−1 . At resonance the voltage across L is

4×10−3V

2.5×10−2V

40V

250V

Current, I=ZE​ where, E=VR2​+(VL​−VC​)2​ Z=R2+(XL​−XC​)2​ At resonance, XL​=XC​ ∴ Z=R Again at resonance, VL​=VC​ ∴ E=VR​ ∴ I=RVR​​=1×103100​= 0.1A ∴VL​=ILω=CωI​=(2×10−6)×(200)0.1​ ∴ VL​=250V .

Q. In a series resonant $L CR$ circuit, the voltage across $R$ is $100 V$ and $R = 1 k Ω$ with $C = 2 μ F$ . The resonant frequency $ω$ is $200 r a d s^{- 1}$ . At resonance the voltage across $L$ is

$4 \times 1 0^{- 3} V$

$2.5 \times 1 0^{- 2} V$

$40 V$

$250 V$