2_7 - Solutions 2.7-Page 176 Problem 1 In the circuit of...

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Solutions 2.7-Page 176 Problem 1 In the circuit of Fig. 2.7.7, suppose that 5 = L H, = 25 R , and that the source E of emf is a battery supplying 100 V to the circuit. Suppose also that the switch has been in position 1 for a long time, so that steady current of 4A is flowing in the circuit. At time , the switch is thrown to position 2, so that 0 = t 4 ) 0 ( = I and 0 = E for t . Find . 0 ) ( t I It is given that describes the circuit. Substituting given information yields: ) ( t E RI I L = + 0 25 5 = + I I Separating variables and integrating yields: t e K I K t I dt I dI 5 ~ 5 ln 5 = + = = ∫∫ The initial condition is used to solve for the integration constant as follows: 4 ) 0 ( = I = = = 4 ~ ) 1 ( ~ 4 ) 0 ( K K I t e I 5 4 =
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Problem 3 Suppose that the battery in Problem 2 is replaced with an alternating current generator that supplies a voltage of volts. With everything else the same, now find . t t E 60 cos 100 ) ( = ) ( t I The differential equation describing the circuit is 5 t I I 60 cos 100 25 = + .
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2_7 - Solutions 2.7-Page 176 Problem 1 In the circuit of...

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