Question

An LCR circuit is at resonance with 10V each across L ,C and R. If the resistance is halved, the respective voltages across L, C and R are
A) 10V,10V,5V
B) 10V, 10V, 10V
C) 20V, 20V, 5V
D) 20V, 20V, 10V
(the answer is d but dont know how)

Answer 1

Explanation:

So We Know,

In LCR Circuit,

Resonance Frequency

fr=

$\frac{1}{2\pi \sqrt{lc} }$

And Resonance occur when

Inductive reactance =Capacitive Reactance

XL=Xc

$lw = \frac{1}{cw}$

So if Resistance is Half

We know,

R=VI

$\frac{r}{2i} = 10$

R=20I

We Know,

Total Resistance called Impedance of LCR Circuit=

$\sqrt{ {r}^{2} + ({xl - xc})^{2} }$

At Resonance,

XL=Xc

Z=

$\sqrt{ {r}^{2} }$

so

Z=R

Impedence is Half and Capacitive reactance and Inductive reactance is double.

Mathematically,

Vr=

$2i \times \frac{r}{2}$

Vr=IR

Vr=V

Vr=10V(Resistor)

VL =2i×XL=2×10=20V

similarly,

Vc=2i×Xc=2×10=20V

so In thisWay

D is correct answer

Hope it Helps you!!