Question

Please write clearly, and show steps for the solution (The answers are shown just to check)

6. For the circuit shown, the voltage source supplies a voltage v(t)= 20 cos(1000t) V. a) Find the equivalent impedance Z as seen by the voltage source. Ans: 2.4 + 214.8 i(t) ► 10mH 0000 b) Determine i(t), and the voltage across the 10 mH inductor. i(t) = 1.33 cos(1000t - 80.8) Find the voltage across the resistor as a function of time. v(t) 6mH S1202

Answer 1

o ] given Silt) 10mH லை vlt) 7 GMH 34 {12r v(t)= 20 COS(1000t) Voit 5 w = 1000 rad/sec XL, = jw he = ; 103xloxios = jsou X1g = jwbn = 3103x6x103 = jan Now z = x2, + X-2 X 12 XL₂+12 z 16X 12 = slot je+12 => jio+ 72296 Z-j1 + 372 13.416/26.56 13.416/2656 z= j10+ 5.366/63.44 Z=j10+ 2.4+; 4-8 z= 124 +; 14.) viti 20 COS 1000+ i(t)= Z 2.4+j14.8

20 COS 1000 t i(t) = 15_80.78 ali(t) = 1333 cos (1000t-80-7817 NOW V(t) = ilt) x X2 U2, (+) = 1.333 cos(10oot - 80.78] xj 10 VL (+) = 1.333 cos (1000 t-80187 X10190 Vin(t) = 13.33 cos (1000 - 50.78+90] V44) = 1333 cos (1000 +9:22] volt . caluculaty above 5) Velt) = ict) x ( 412 || 121 Velt) = 1-333 cos(1000+ -80-78] « [s.366 463.44] Velt) = 7,1528 Cos (1000t-80.78 +63.447 Velt) = 7:4526 cos (1000+ - 11-34'] volt)