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
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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,
Step 2
From the above Given Current v/s driving frequency graph:
We have,
So,
The Values of each given parameters are calculated as follows:
a) Resistance (R)
We know that,
At Resonance Condition:
So,
Here,
Step 3
b) Capacitance (C):
We know that,
Capacitive Reactance
Here,
Since we know that at resonance condition:
As per the above relation, we get:
Step by step
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