(a) Explanation Given information: The time ( t ) is 0 when switch is closed. The capacitor is C . Calculation: Show the circuit in mechanical system and electrical system as in Figure (1). The mechanical analogue of closing a switch S is the sudden application of a constant force of magnitude P to the mass. Show the diagram of the block with the forces acting as Figure (2). The final value of the current corresponds to the final velocity of the mass, since the capacitance is zero the spring constant is also tends to zero. The expression for the forces acting on the block in vertical direction as follows: P − c d x d t = m d 2 x d t 2 (1) But the final velocity occurs when d 2 x d t 2 is equal to zero. Substitute 0 for d 2 x d t 2 (b) To determine The time ( t ) at which the current will have reached ( 1 − 1 e ) times its final value.

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 19.5, Problem 19.154P

(a)

To determine

The final value of the current (ifinal) in the circuit.

(b)

To determine

The time (t) at which the current will have reached (1−1e) times its final value.

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Chapter 19.5, Problem 19.153P

Chapter 19.5, Problem 19.155P

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Vector Mechanics for Engineers: Statics and Dynamics

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The final value of the current ( i f i n a l ) in the circuit.

Solution Summary: The author shows the circuit in mechanical system and electrical system as in Figure (1). The final value of current corresponds to the final velocity of the mass.