Explanation Calculation: The given diagram is shown in Figure 1 The conversion from μ F into F is given by 1 μ F = 10 − 6 F The conversion from k Ω into Ω is given by, 1 k Ω = 10 3 Ω The conversion from 15 k Ω into Ω is given by, 15 k Ω = 15 × 10 3 Ω The conversion from 30 k Ω into Ω is given by, 30 k Ω = 30 × 10 3 Ω The conversion from 1 msec into sec is given by, 1 msec = 10 − 3 sec The conversion from 1.5 msec into sec is given by, 1.5 msec = 1.5 × 10 − 3 sec The conversion from 10 msec into sec is given by, 10 msec = 10 × 10 − 3 sec The equivalent circuit for the case when the switch is closed is shown below. The required diagram is shown in Figure 2 To obtain the value of the equivalent circuit, short circuit the voltage, open circuit the capacitor terminals and redraw the circuit. The required diagram is shown in Figure 3 From above, the equivalent resistance of the circuit is calculated as, R e q = R 1 | | ( 15 × 10 3 Ω ) | | R 2 | | ( 30 × 10 3 Ω ) R e q = R 1 | | R 2 | | ( 15 × 10 3 Ω ) ( 30 × 10 3 Ω ) ( 15 × 10 3 Ω ) + ( 13 × 10 3 Ω ) R e q = R 1 | | R 2 | | ( 10 × 10 3 Ω ) 1 R e q = ( R 1 ) + ( R 2 ) ( R 1 ) ( R 2 ) + 1 ( 10 × 10 3 Ω ) Solve further as, 1 R e q = ( ( R 1 ) + ( R 2 ) ) ( 10 × 10 3 Ω ) + ( R 1 ) ( R 2 ) ( R 1 ) ( R 2 ) ( 10 × 10 3 Ω ) ...... (1) The expression for the time constant is given by, τ = R e q C ...... (2) Substitute 1.5 × 10 − 3 sec for τ and 1 × 10 − 6 F for C in the above equation. 1.5 × 10 − 3 sec = R e q ( 1 × 10 − 6 F ) R e q = 1500 Ω Open the switch and redraw the circuit

Principles and Applications of Electrical Engineering

6th Edition

ISBN: 9780073529592

Author: Giorgio Rizzoni Professor of Mechanical Engineering, James A. Kearns Dr.

Publisher: McGraw-Hill Education

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Chapter 5, Problem 5.47HP

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The value of the resistance R 1 and R 2 .

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