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Equation of emf of a generator is `V = 282 sin 100 pi t` volt. Internal resistance of generator is `2000 Omega`. It is connected as shown in Fig. Find the frequency of generator and impedance of circuit. |
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Answer» Here, `V = 282 sin 100 pi t, R = 2000 Omega` `L = (40)/(pi) H` and `C = (10)/(pi) mu F . V = ? , Z = ?` The standard form of alternating emf is `E = E_(0) sin omega t`. Compare it with `V = 282 sin 100 pi t`, to get `E_(0) = 282 V, omega = 2 pi v = 100 pi`, `v = (100)/(2) = 50 Hz` `X_(L) = omega L = 2 pi v xx (4)/(pi)` `= 2 xx 50 xx 40 = 4000 ohm` `X_(C ) = (1)/(omega C) = (1)/(2 pi v C)` `(1)/(2 pi xx 50 xx (10)/(pi) xx 10^(-6)) = 1000 Omega` `Z = sqrt(R^(2) + (X_(L) - X_(C ))^(2))` `= sqrt((2000)^(2) + (4000 + 1000)^(2))` `= 10^(3) sqrt( 4 + 9) = 3.6 xx 10^(3) Omega` |
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