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(a) At resonant frequency
ω= 1
√ LC
2 πf = 1
√LC
4 π 2 f 2= 1
LC
C= 1
4 π2 f 2 L
C= 1
4 π2 ×8 ×1982 ×103
C=9.79 ×10−11
Value of v2
¿ v1 × rms
R × 1
ωc
¿ 100 μv
300 × 1012
2 π × 198× 103 × 79.7
¿ 100 × 106
30× 2 π ×198 ×103 ×79.7
¿ 3.361× 10−2 V
¿ 0.03361 V
(b) L= μ N2 A
μ

N2= Lμ
μA ; N = √ Lμ
μA
N= √ 8 ×10−3 ×50 × 10−3
1.256629× 10−6 × π ×7.5 ×10−3 ×7.5 × 10−3
¿ √ 400× 10−6
222 ×10−12 ; → √ 400
222 ×106
N=1.342 ×103=1342
In case of rod of manganese zinc
N= √ 6 × 10−3 × 50 ×10−3
6 ×10−4 × π × 7.5 ×10−3 ×7.5 ×10−3
N= √ 0.29294 × 104
N=0.53× 102 ;=53
(c)
C1= 1
4 π2 f 1
2 L = 1
4 π 2 ( 148 )2 ×106 ×8 ×10−3
C1=1.4267 ×10−10
C1=142.67 pico farad
C2= 1
4 π2 f 2 L= 1
4 π 2 × ( 248 ) 2 ×106 × 8 ×10−3
C2=5.08 ×10−11 ;5.08 pico farad

References

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