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In a series L-R circuit (L=35 mH and R=1...

In a series L-R circuit `(L=35 mH and R=11 Omega)`, a variable emf source `(V=V_(0) sin omega t)` of `V_(rms)=220V` and frequency 50 Hz is applied. Find the current amplitude in the circuit and phase of current with respect to voltage. Draw current-time graph on given graph `(pi=22/7)`.

Text Solution

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Here, `L = 35 mH = 35 xx 10^(-3) H, R = 11 Omega`
`E_(v) = 220 V, (omega)/(2 pi) = 50 Hz = v`
`X_(L) = omega L = 2 pi xx 50 xx 35 xx 10^(-3) = 11 ohm`
Impedance of the circuit
`Z = sqrt(R^(2) + X_(L)^(2)) = sqrt(11^(2) + 11^(2)) = 11 sqrt2 ohm`
`E_(0) = sqrt2 E_(v) = sqrt2 xx 220 V`
`I_(0) = (E_(0))/(Z) = (sqrt2 xx 220)/(11 sqrt2) 20 A`
If `phi` is phase difference between current and voltage, then
`tan phi (X_(L))/(R ) = (11)/(11) = 1`
`phi = pi//4` or `45^(@)`
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