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AN LIKC CIRCUIT HAS A VARIAALE FCQUENCY POWER SUPNLY WITH V Vs. DRIVING FREQUENCY GRAPH IS. SHOWN. = 20V. ITS CURRENT RMS IRMSLA) 15 THE RMS CURRGNT AMPLITUDG. IF THe INDUCTANLE IN THE CIRCUIT 13 3 HENKIGS, FIND: fCH2) 1. 500 a) b)c c) Xe if 2) X IF f = S0OH2 e) Z f= SOOHZ (1

AN LIKC CIRCUIT HAS A VARIAALE FCQUENCY POWER SUPNLY WITH V Vs. DRIVING FREQUENCY GRAPH IS. SHOWN. = 20V. ITS CURRENT RMS IRMSLA) 15 THE RMS CURRGNT AMPLITUDG. IF THe INDUCTANLE IN THE CIRCUIT 13 3 HENKIGS, FIND: fCH2) 1. 500 a) b)c c) Xe if 2) X IF f = S0OH2 e) Z f= SOOHZ (1

Question
### LRC Circuit Analysis **Problem Statement:** An LRC circuit has a variable frequency power supply with \( V_{rms} = 70 \, V \). Its current versus driving frequency graph is shown below. **Graph:** - The vertical axis represents the current \( I_{rms} (A) \). - The horizontal axis represents the frequency \( f (Hz) \). - The graph depicts a peak at approximately \( f = 500 \, Hz \). **Objective:** Determine various components of the circuit given that the inductance in the circuit is 3 henries. **Components to Find:** a) Resistance (\( R \)) b) Capacitance (\( C \)) c) Capacitive reactance (\( X_c \)) if \( f = 500 \, Hz \) d) Inductive reactance (\( X_L \)) if \( f = 500 \, Hz \) e) Impedance (\( Z \)) if \( f = 500 \, Hz \) Use the given information and graph to calculate the requested values, taking note of peak resonant frequency and its significance in LRC circuits.
Transcribed Image Text:### LRC Circuit Analysis **Problem Statement:** An LRC circuit has a variable frequency power supply with \( V_{rms} = 70 \, V \). Its current versus driving frequency graph is shown below. **Graph:** - The vertical axis represents the current \( I_{rms} (A) \). - The horizontal axis represents the frequency \( f (Hz) \). - The graph depicts a peak at approximately \( f = 500 \, Hz \). **Objective:** Determine various components of the circuit given that the inductance in the circuit is 3 henries. **Components to Find:** a) Resistance (\( R \)) b) Capacitance (\( C \)) c) Capacitive reactance (\( X_c \)) if \( f = 500 \, Hz \) d) Inductive reactance (\( X_L \)) if \( f = 500 \, Hz \) e) Impedance (\( Z \)) if \( f = 500 \, Hz \) Use the given information and graph to calculate the requested values, taking note of peak resonant frequency and its significance in LRC circuits.
Expert Solution
Step 1

Solution:

 

Given Values,

RMS Voltage (VRMS)=20 VInductance (L)=3 H

Step 2

From the above Given Current v/s driving frequency graph:

 

We have,

 

RMS current (IRMS)=5 AResonant frequency (fr)=500 Hz

 

So,

 

The Values of each given parameters are calculated as follows:

 

a) Resistance (R)

 

We know that,

 

At Resonance Condition:

 

XL=XC which occurs at 500 Hzand Z=R (Frequency at resonance for Z wil be 0)

So,

 

Here,

 

Z=R=VRMSIRMSR=20 V5 A=4 ΩThus,Resistance (R)=4 Ω

 

 

 

Step 3

b) Capacitance (C):

 

We know that,

 

Capacitive Reactance(XC)=1ωC

 

Here,

 

C=1ωXCC=12πfrXC

 

Since we know that at resonance condition:

 

XC=XLXL=ωL    =2πfrL    =2×3.14×500 Hz×3 H    =9420 ΩHence,XC=XL =9420 Ω

 

As per the above relation, we get:

C=12πfrXC  =12×3.14×500 Hz×9420 ΩC=3.38×10-8 F =33.8 nFThus,The capacitence Value is  33.8 nF

 

 

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