# Solved Problems-16

Problems-16

**A voltage of**

*v*= 2000 sin*Ï‰*

**t****+ 400 sin 3**

*Ï‰*

**t****+ 100 sin 5**

*Ï‰*

**t****is applied to a series circuit having**Î©

*R*= 10**and**

*C*= 30**Î¼F and a variable inductance.**

**Find the value of inductance so as to give resonance at 3**^{rd}harmonic frequency.**What are the r.m.s. values of voltage and current with this inductance in circuit? Take***Ï‰***= 300 rad/s.**

Solution

Here,

*Ï‰*= 300 rad/s,*R*= 10 Î©,*C*= 30 Ã— 10^{â€“6}Fâˆ´ Resonant frequency

*Ï‰*_{0}= 3 Ã—*Ï‰*= 900 rad/s- âˆµ

**(**

__For 1__^{st}Harmonic*Ï‰*= 300 rad/s):

âˆ´

âˆ´

**(**

__For 3__^{rd}Harmonic*Ï‰*= 900 rad/s):

âˆ´

âˆ´

âˆ´

**(**

__For 5__^{th}Harmonic*Ï‰*= 1500 rad/s):

âˆ´

âˆ´

âˆ´ RMS value of the current,

âˆ´ RMS value of the voltage,