Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web: Ph:

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1 Serial : LS_N_A_Network Theory_098 Delhi Noida Bhopal Hyderabad Jaipur Lucknow ndore Pune Bhubanewar Kolkata Patna Web: info@madeeay.in Ph: CLASS TEST 08-9 NSTRUMENTATON ENGNEERNG Subject : Network Theory Date of tet : /09/08 Anwer Key. (c) 7. (d) 3. (b) 9. (a) 5. (d). (d) 8. (c) 4. (d) 0. (b) 6. (b) 3. (b) 9. (b) 5. (a). (c) 7. (b) 4. (b) 0. (d) 6. (c). (c) 8. (b) 5. (b). (b) 7. (d) 3. (a) 9. (c) 6. (b). (b) 8. (d) 4. (c) 30. (b)

2 8 ntrumentation Engineering Detailed Explanation. (c) deal voltage ource ha zero internal reitance, Time contant τ RC 0 Hence capacitor will charge intantaneouly.. (d) The time contant τ R eq C eq Here, R eq R R /3 R and C eq C C 3C τ 3 3 R C RC 3. (b) n order to inject the 00 C charge to the 50 ource the current in the loop mut be anticlockwie 30 i 0 Ω 50 Q 00 i.67 A t 60 applying KL in the circuit 0i (0 i 0) (b) For power tranfer to be maximum R L R Th Redrawing the circuit R Th OC OC - open circuit voltage SC 60 6 Ω v x Ω vx a Open Circuit b OC v x Applying KL in loop 6 v x (i) v x...(ii)

3 CT-08 N Network Theory 9 Solving thee, 5 A OC v x Ω a SC SC 60 0 A 6 60 Ω Short circuit R Th 0 R L Ω 0 b 5. (b) The equation of line paing through origin i y m x y y t x x m t T0 m t T the intantaneou power for 0 t T 0 i p(t ) 0 mt T 0 0 t < 0.5T0 R T t < T 0 0 P avg, oberving that the fundamental period i T 0, we have P avg P avg 0.5T0 4m t dt T 0 0 T0 R m 6R 0.5 T 3 0 m t R 0 4 T 6. (b) On careful obervation, we find ; ; Uing the ame logic, we try to work out the miing number a and To verify the correctne, we check (d) Z() LC RC 0 for pole to be real (RC) 4LC 0 RC ( R L) C LC ( R L) C R L R L LC RC C R L C

4 0 ntrumentation Engineering 8. (c) Two Port Network 4 Ω overall Z 0 putting Z Ω (b) Under teady tate L 0 5 R R R C L R 0 R R Energy tored in capacitor Energy tored in inductor C c L L 6 0R R R or R 5 Ω 5A Ω C L 0. (d) Given circuit, Ω Ω 0 i 30 8 Ω 4 A 3 0

5 CT-08 N Network Theory By applying nodal analyi, () and () Subtituting () in () 3( 4) Current upplied by dependent ource i A Power delivered 3 0 i 30 (3 6) (4) 7 W. (b) at reonance, X L X C Current through L i identical to current through C. X π fl L L C where f π LC C π L L π LC A. (b) Conidering one unit /...(i) and ( ) from equation (i) and (ii)...(ii)

6 ntrumentation Engineering and Two uch unit are connected in cacade (b) For t < 0 0 Ω A 0 Ω k k L L 0 6H H A L 0.5 A 8 At t 0 L A 8 Applying KL (0 5) 0.5 L L 3.75 olt 5 Ω 0 Ω L 0.5 A 4. (d) Power conumed in 5 Ω reitor 0 W P 0 R 5 A Total power conumed in reitor 5 Ω and 0 Ω ( ) [5 0] 30 W Total power upplied by ource 50 50W Power factor Since it i an R-L circuit, the power factor i lagging. 5. (a) oc

7 CT-08 N Network Theory 3 0 Ω 0 Ω 6 0 Ω 0 oc 6. (c) c 0 A 0 0 R Th oc 0 Ω c P max Z ( oc) 0 4R 5 W Th Redrawing the circuit and open circuiting the port Z 0 Ω 0 0 Ω 0 Ω 0 Ω 0 5 Ω 0 c 7. (d) From the firt circuit i 3 6 3i...() From the econd circuit, Power acro 0 Ω 90 W. i L 0 90 i L 9 3A. a.5 Ω 5 Ω Ω 0 3 Ω 6 Ω 6 a 5 Ω 0 Ω i i 6 a i L i 6a i L 3 6 A Hence 6 a 6 a From the figure, a i i So, i A From equation () 0 3i 3 3

8 4 ntrumentation Engineering 8. (d) Redrawing the circuit R Th : x 0 0 g m x R 0 R R R 0 3 R 3 x R g R m x a 0 0 ( m ) ( ) 0 g R 0 R R R 3 0 R b R Th 0 0 R3( R R) ( g R ) R ( R R ) m 3 9. (a) From the given figure. Z Z Z Z Z Z The above equation can be rearranged a (Z Z ) Z ( )... (i) (Z Z ) (Z Z ) Z ( )... (ii) generator equivalent i Z Z Z Z ( ) Z Z Z 0. (b) Redrawing the circuit 50 Ω ( b ) 0 Ω 0 Ω b a 4 b Ω (0. a ) A 0. a Applying KL 50 a 40( 0. a ) (i) ( b ) 0 a... (ii) a 0 b 4 b 0... (iii) By equation (i), (ii) and (iii) b 0.96 A.

9 CT-08 N Network Theory 5. (c) Putting 0 Applying KCL at node A h x x x 0 0 x x x Ω 0 Ω A 50 Ω 00 Ω x 0 x 0 x h 85 Ω. (c) 0...(i) 0....(ii) For maximum power tranfer 0 Ω Port Network Z Th From equation (i), (ii) and (iii), we get R L Z Th 0...(iii) Z Th 7.5 Ω 0 Ω 00 Port Network OC (iv) when 0...(v)

10 6 ntrumentation Engineering OC 5 Maximum power tranferred OC 4Z Th (5) W. 3. (a) For t 0 Energy tored at t 0 i 0 A 0 40 i L (0 ) i L (0 ) A 0 0 Ω 0 H 40 Ω J L i ( ) At t 0 (0 R) L 0 R 40 Ω τ L R eq 0 0.ec ( ) R Ω 0 Ω A 40 Ω i(t) e 0t A At t t 90% energy i diipated remaining energy 0 0 Joule 00 ( ) L i t 5 i (t ) i (t ) i(t ) 0t e 0.4 t 0.5 ec 5. mec 4. (c) Q(0 ) C(0 ) (0 ) Q(0 ) 90 µ 3 C 30 µ kω 8 kω ( ) (8 8)k k 8 9 u( t) 8 kω τ t / oltage acro capacitor ( ) (0 ) ( ) e ( ) τ C(k (8 8)k) τ ec

11 CT-08 N Network Theory 7 (t) 75 t e (0 mec) e 3.85 Q(0 mec) µ 5.5 mc 5. (d) h h h h (i) 0 A, A, 4.5,.5 h h (ii) 4 A, 0, 6,.5 h h 0 h h 0.5 h h 6 h h Ω h parameter matrix i (b) For t < 0: 6 Ω 60 The equivalent circuit i 6 Ω 40 6 Ω 0 / H 0 i(t) R eq 6 (6 6) v(t) R eq 4 Ω R eq 6 6 4Ω 60 0 i(0) 4 Hence i(0 ) 0 A. (0 ) A 60 / H i(t) 0

12 8 ntrumentation Engineering For t > 0: 6 Ω 6 Ω 6 Ω i(t) H 0 8 F The equivalent circuit i 4 Ω i(t) H i (t) 40 8 F 0 Applying Laplace tranform to the above circuit () 4 () () () () Ω () () () 8 6 (40 0 ) () () 8 6 () 0 ( 4) By applying invere Laplace tranform i(t) 0e 4t A

13 CT-08 N Network Theory 9 7. (b) 0 Ω 0 Ω A 0 0 Ω 0 Ω 0 Ω 0 Ω B R in Th : R in 0 0 (0 0 0) 0 R in 7.5 Ω 0 A A 7.5 Th AB R Th : 0 0 Ω 0 Ω 0 Ω 0 Ω R Ω 0 Ω 0 Ω R Th R th 80 0 Ω R 0 Ω R th 0 Ω Maximum power can be tranferred 8. (b) H() Th mw 4R 4 80 Th Y () X ()

14 0 ntrumentation Engineering x( t) inωt / Ω Ω Ω yt () Ain( ωt 45 ) Y() () ( Ω) () () Y () X () H() H(jω) H(jω) X () ( ) X( ) () 4 jω j ω j jω ω H(jω) tan ω ω given, H( jω) 45 ω ω tan () tan ω ω j ω ω ω ω ω ω ω ω 0 ω ± 4() ± 9 ± 3 4 ω 4 rad/ec ω i alway poitive. 4

15 CT-08 N Network Theory 9. (c) For erie reonance X L X C X C X L j Ω j j8 jm X L j0 jk 6 X L j0 j8k j j0 j8k j j8k ( M k LL) k (b) Conidering only DC ource 0 i R () t Ω i R (t) 0 5 A Conidering only AC ource H j Ω / j Ω i R (t) i(t) i(t) j i() t j 5cot A j ( j ) 5cot 5cot A j 4 j( j) 0.5j 0.5j j 4 4 i R () t Ω i 5 cot i(t) A 8( j j) 0.5j j 0.5j A 0.5j i R (t) 5 0 j A 0.5 j ( j) (.8) i R (t) A when both the ource are acting imultaneouly, i R (t) co (t 8.44 ) A