Question
Question: In the figure which voltmeter reads zero, when \( \omega \) is equal to the resonant frequency of th...
In the figure which voltmeter reads zero, when ω is equal to the resonant frequency of the series LCR circuit?
A). V1
B). V2
C). V3
Solution
An LCR circuit has three major components: resistor, inductor, capacitor.
These components can be connected in either a series or a parallel configuration.
Impedance is lowest at resonance in the LCR series. As a result, Zmin=R . ω is the angular frequency.
Complete Step By Step Answer:
A voltmeter will read zero when the points being measured are of the same potential.
Let the voltage across the inductor be VL and voltage across the capacitor be VC .
Voltage across the resistor is given by V1=IR , where I is the current and R is the resistance.
Voltage across inductor and capacitor is given by V2=VL−VC
Therefore voltage across V3 is given by V32=V12+(VL−VC)2
Only the presence of resistor affect the voltage through the voltmeter V1 , the inductor and the capacitor affect the voltage through the voltmeter V2 , all three components affects the voltage through the voltmeter V3
Since the resonance voltage across the inductor and capacitor will be the same.
That is VL=VC
⇒VL−VC=0
⇒ voltage across the voltmeter V2 will be zero.
The correct answer is option B, V2 .
Note:
The frequency at which the impedance of the LCR circuit becomes minimal or the current in the circuit becomes maximal is known as the resonance frequency.
Resonant frequency ωr==LC1
LCR circuits have a significant amount of resonance. Energy can be stored in LCR circuits in two ways: as an electric field in a capacitor when it is charged, or as a magnetic field in an inductor when current runs through it.