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Question

In the adjoining ac circuit, the voltmeter whose reading will be zero at resonance is

1817760


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Solution

Impedance and voltage at resonace

  1. We know the impedance of an LCR circuit is expressed by the form, Z=R2+ωL-1ωc2, where R is the resistance, 1ωc is the capacitive reactance, and ωLis the inductive reactance.
  2. But at resonance, the capacitive reactance = inductive reactance, i.e, 1ωc=ωL.
  3. So at resonance total impedance = total resistance, i.e, Z = R.
  4. From Ohm's law, voltage = IR, but net impedance across the inductor and capacitor is zero. So at resonance net voltage across the inductor and capacitor is zero.

Diagram

1817760

Therefore, at resonance net voltage across the inductor and capacitor is zero.


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