If resistance R=100Ω , inductance L=(2/π )H and capacitance C=(8/π )Î¼F are connected in series with an AC source of 200volt and frequency f as shown in the circuit. If the readings of the hot wire voltmeters V1 and V2 are same then which among the following statements is wrong?

Question

If resistance R=100Ω , inductance L=(2/π )H and capacitance C=(8/π )Î¼F are connected in series with an AC source of 200volt and frequency f as shown in the circuit. If the readings of the hot wire voltmeters V1 and V2 are same then which among the following statements is wrong? <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-xvp9afg2gmovpnqe.jpg" /> (A) f=125 Hz (B) f=250 π Hz (C) current through R is 2A (D) V1= V2= 1000 volt

Tardigrade Admin · Accepted Answer

V1=V2 ⇒ xL=xc ⇒ f=(1/2 π √LC)=125 Hz I0=(V0/R)=(200/100) (.∵ x=0 ∴ z=R.) =2A V1=V2=1X=1.(.ÏL.)=2× 2π × 125× (2/π ) V1=V2=1000 volt

$f = 125 Hz$

$f = 250 π Hz$

current through $R$ is $2 A$

$V_{1} = V_{2} = 1000 v o lt$

$V_{1} = V_{2}$ $\Rightarrow x_{L} = x_{c}$
$\Rightarrow f = \frac{1}{2 π L C} = 125 Hz$
$I_{0} = \frac{V _{0}}{R} = \frac{200}{100}$ $(∵ x = 0 ∴ z = R)$
$= 2 A$
$V_{1} = V_{2} = 1 X = 1. (ω L) = 2 \times 2 π \times 125 \times \frac{2}{π}$
$V_{1} = V_{2} = 1000 v o lt$

Q. If resistance R=100Ω , inductance L=π2​H and capacitance C=π8​μF are connected in series with an AC source of 200volt and frequency f as shown in the circuit. If the readings of the hot wire voltmeters V1​ and V2​ are same then which among the following statements is wrong?

f=125Hz

f=250πHz

current through R is 2A

V1​=V2​=1000volt

V1​=V2​ ⇒xL​=xc​ ⇒f=2πLC​1​=125Hz I0​=RV0​​=100200​ (∵x=0∴z=R) =2A V1​=V2​=1X=1.(ωL)=2×2π×125×π2​ V1​=V2​=1000volt

$f = 125 Hz$

$f = 250 π Hz$

current through $R$ is $2 A$

$V_{1} = V_{2} = 1000 v o lt$

$V_{1} = V_{2}$ $\Rightarrow x_{L} = x_{c}$
$\Rightarrow f = \frac{1}{2 π L C} = 125 Hz$
$I_{0} = \frac{V _{0}}{R} = \frac{200}{100}$ $(∵ x = 0 ∴ z = R)$
$= 2 A$
$V_{1} = V_{2} = 1 X = 1. (ω L) = 2 \times 2 π \times 125 \times \frac{2}{π}$
$V_{1} = V_{2} = 1000 v o lt$