PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB
230 Practical MATLAB® Applications for Engineers because P = i(t)^2 R, then the effective current is given by I tt itdt t t ...
Alternating Current Analysis 231 where V T RMS vtdt T (^12) 0 () ∫ and I T itdt T MS pt dt TT R PAVG (^12) 00 () ( ∫∫ and 1 ...
232 Practical MATLAB® Applications for Engineers since T = 1/f, then W VI R f RMS RMS (in joules) R.3.22 The reactive power Q ...
Alternating Current Analysis 233 Observe that the phase angle θ between the current iR(t) and the voltage vR(t) in a resistive c ...
234 Practical MATLAB® Applications for Engineers R.3.29 Let us assume that the voltage across the capacitor C is vC(t) = Vm cos( ...
Alternating Current Analysis 235 or vt()ImLR^22 Xcos( t) where θ = tan−^1 (XL/R) Note that |Z| = (^) √ R^2 + XL^2 (in ohms) ...
236 Practical MATLAB® Applications for Engineers ANALYTICAL Solution XL = jL = j (^1000) 0.02 = j20 X j C j C j ...
Alternating Current Analysis 237 where G = 1/R then i(t) = Vm|Y| cos(t + ) where θ = tan−^1 (−R/ωL). Clearly, the voltage v(t) ...
238 Practical MATLAB® Applications for Engineers Part b V I Y T T 15 20 89 10 26 6 3 168 6 6 ∠ ∠ ∠ *. . I V R R ...
Alternating Current Analysis 239 v(t) I L sin t I C m m sin( t) () or v(t) = XIm cos(t + θ) where the total reactance ...
240 Practical MATLAB® Applications for Engineers Indicate also the type and its equivalent circuit in term of its simplest eleme ...
Alternating Current Analysis 241 where tan 1 ()^1 22 LC R for Clearly, a. If ωL > 1/ωC, then ...
242 Practical MATLAB® Applications for Engineers R.3.45 Let us evaluate now the current i(t) of the parallel RLC circuit diagram ...
Alternating Current Analysis 243 ANALYTICAL Solution ZRjXTL 34 34j ^4 3 (^22) ∠ 1 tan ZT = 5 ∠53.13° I V ZT ...
244 Practical MATLAB® Applications for Engineers or SV IRMS RMS*(10 0∠∠)( 2 53 13. )20 53 13∠.va The power triangle for t ...
Alternating Current Analysis 245 and Q = |S|sin( ) = (^150) * 0.809 = 121.2 var R.3.49 Let us revisit the RLC series circuit sho ...
246 Practical MATLAB® Applications for Engineers and 2 2 1 1 22 R S R QQS rad/s if QS > 10 then ω 1 = ωR ( ...
Alternating Current Analysis 247 and 2 2 2 2 1 2 1 2 1 2 114 R RC RC C R R C L The BW is then ...
248 Practical MATLAB® Applications for Engineers for DC circuits can easily be extended to include AC circuits. To use the mesh ...
Alternating Current Analysis 249 The matrix loop equation is indicated as follows: 82 3 0 385 5 0572 10 0 0 1 2 3 j ...
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