Question

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)`.

Answer 1

`X_(L) = omega(L) = 2pi xx 50 xx 35 xx 10^(-3)`
`= 3.5 xx (22)/(7) = 11Omega`
`R =11Omega`
Impedance `Z = sqrt(R^(2) + X_(L)^(2)) = 11sqrt2Omega`
`i_(rms) = (V_(rms))/(Z) = (220)/(11sqrt2) = (20)/sqrt2 A = 10 sqrt2A`
Peak current `i_(0) = sqrt2 i_(rms) = sqrt2 xx 10sqrt2 = 20 A`
Phase difference between voltage and current
`tan phi = X_(L)/(R) = (11)/(11) =1 implies phi = (pi)/(4)`
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