Derive the expression of quality factor of series R-L-C circuit at resonance.
The quality factor is , in general, defined as the ratio of resonant frequency to bandwidth. It is given by
\(Q=\frac{f_r}{(f_2-f_1)}=\frac{2\pi L}{R}\left(\frac{1}{2\pi\sqrt{LC}}\right)\)
\(Q=\frac{1}{R\sqrt{LC}}\)
Thus the quality factor, Q can be improved by decreasing the resistance, R or increasing the ratio of inductance to capacitance L/C.
In a series RLC circuit resonance can be obtained by varying f, that is adjusting the values of L and C. In radio receiver, capacitance is varied to tune different radio station so that resonance is obtained at the desired frequency.
Q is also a measure of the degree of sensitivity of the circuit.
A flux of 0.0006Wb is required in the air – gap of an iron ring of cross – section 5.0 cm2and mean length 2.7 m with an air – gap of 4.5 mm. Determine the ampere turns required. Six H values and corresponding B values are noted from the magnetization curve of iron and given below.
H(At/m) |
200 |
400 |
500 |
600 |
800 |
1000 |
B(Wb/m2) |
0.4 |
0.8 |
1.0 |
1.09 |
1.17 |
1.19 |
Derive the expression of quality factor of series R-L-C circuit at resonance.
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