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Alternating Current question

2004 · Shift 0 · Q148
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Alternating Current question

2004 · Shift 0 · Q148

JEE MainPhysicsAlternating CurrentMCQ+4 / −1
In an LCRLCRLCR series a.c.a.c.a.c. circuit, the voltage across each of the components, L,CL,CL,C and RRR is 50V50V50V. The voltage across the L.CL.CL.C combination will be :
  1. A
    100V100V100V
  2. B
    50250\sqrt 2502​
  3. C
    50V50V50V
  4. D
    0V0V0V (zero)
View written solutionFree

Correct answer: D

  1. In a series LCRLCRLCR circuit, the voltages across the resistor, inductor, and capacitor are phasors:
  • VRV_RVR​ is in phase with current.
  • VLV_LVL​ leads current by 90∘90^\circ90∘.
  • VCV_CVC​ lags current by 90∘90^\circ90∘.

  1. Given: VR=50 V,VL=50 V,VC=50 VV_R = 50\,\text{V}, \quad V_L = 50\,\text{V}, \quad V_C = 50\,\text{V}VR​=50V,VL​=50V,VC​=50V

  2. Since VLV_LVL​ and VCV_CVC​ are exactly opposite in phase, the net voltage across the LCLCLC combination is the phasor difference: VLC=∣VL−VC∣V_{LC} = |V_L - V_C|VLC​=∣VL​−VC​∣

  3. Substituting the values: VLC=∣50−50∣=0 VV_{LC} = |50 - 50| = 0\,\text{V}VLC​=∣50−50∣=0V

  4. Therefore, the voltage across the LCLCLC combination is zero.

So the correct option is: D: 0 V\boxed{\text{D: }0\text{ V}}D: 0 V​

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