TEST3_2008-soln - ) ( t i tr for > t with two...

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Engr 260 -- Circuits & Devices Test 3 April 30, 2008 Name: _ SOLUTION ____________ Part 2: Solve each of the following problems. 1. For the circuit shown, a. Find the equivalent inductance seen by the voltage source. b. Find ) ( t i for 0 > t , if 40 ) 0 ( = i mA. a) mH L eq 60 24 36 40 || 60 16 20 = + = + + = b) () mA t t dt t i dt t v L t i t t t eq 90 4 cos 50 40 4 cos 50 40 4 sin 12 10 60 1 ) 0 ( ) ( 1 ) ( 0 0 3 0 + = + = + × = + = 2. For the given circuit, find: a) ) ( v and ) ( i b) ) 0 ( + v and ) 0 ( + i c) + = 0 t dt di
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3. Find ) ( t v for 0 > t . Ω = = 2 3 || 6 R eq , 4 RC = = τ [] τ + = t - e ) ( v ) 0 ( v ) ( v ) t ( v Using voltage division, V 10 ) 30 ( 6 3 3 ) 0 ( v = + = , V 4 ) 12 ( 6 3 3 ) ( v = + = Thus, 4 t - 4 t - e 6 4 e ) 4 10 ( 4 ) t ( v + = + = 4. For the given circuit the switch has been open for a long time when it was closed at 0 = t . Find the current ) ( t i , for 0 > t , Before t = 0, i is obtained by current division or = + = ) 2 ( 4 4 4 ) t ( i A 1 After t = 0, [] τ + = t - e ) ( i ) 0 ( i ) ( i ) t ( i eq R L = τ , Ω = + = 7 12 || 4 4 R eq 2 1 7 5 . 3 = = τ 1 ) 0 ( i = , 7 6 ) 2 ( 3 4 3 ) 2 ( 12 || 4 4 12 || 4 ) ( i = + = + = t 2 - e 7 6 1 7 6 ) t ( i + = = ) t ( i () A e 6 7 1 2t - 5. In the circuit below, 0 ) 0 ( = v V, and 1 ) 0 ( = i A.
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a) Write an expression for the transient current
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Unformatted text preview: ) ( t i tr for > t with two unknown constants. b) What is the steady-state value of the current i ? c) Find ) ( t i for > t , with all unknown constants evaluated using appropriate initial conditions. The switch has been at position a for a long time and moves to position b at = t . a. Using KVL, derive a differential equation for the current ) ( t i in the circuit. b. By trying an exponential solution of the form st Ae t i = ) ( , prove that the resulting characteristic equation is of the form 1 2 = + + LC s L R s . c. Write an expression for the current ) ( t i based on the roots of the characteristic equation. d. Find ) ( t i for > t ....
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TEST3_2008-soln - ) ( t i tr for > t with two...

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