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2. Show that a ohm · farad is the same as a second. Show steps. 3. A 3 µF capacitor initially has a voltage of 1.5 V when it is discharged through a resistance R. The voltage 3 ms after it has started to discharge is 0.25 Volts. a. Determine the time constant tc. b. Determine the resistance R.

2. Show that a ohm · farad is the same as a second. Show steps. 3. A 3 µF capacitor initially has a voltage of 1.5 V when it is discharged through a resistance R. The voltage 3 ms after it has started to discharge is 0.25 Volts. a. Determine the time constant tc. b. Determine the resistance R.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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2. Show that a ohm · farad is the same as a second. Show steps. 3. A 3 µF capacitor initially has a voltage of 1.5 V when it is discharged through a resistance R. The voltage 3 ms after it has started to discharge is 0.25 Volts. а. Determine the time constant Tc. b. Determine the resistance R.
Transcribed Image Text:2. Show that a ohm · farad is the same as a second. Show steps. 3. A 3 µF capacitor initially has a voltage of 1.5 V when it is discharged through a resistance R. The voltage 3 ms after it has started to discharge is 0.25 Volts. а. Determine the time constant Tc. b. Determine the resistance R.
Discharging Capacitor: Kirchoff's loop rule applied to the discharging capacitor circuit gives R > AV: = IR – Δν C loop The current is leaving the positive plate so I = – dQ/dt = -C DAV-//dt. -c dAVc/dt. C Substituting this into loop rule gives a differential equation for Q (t): dVe RC + V = 0 dt This is the simplest differential equation you will learn in your differential equations class. The solution for the differential equation for V.(t) is an exponential: V.(t) = Ve-t/(RC) (discharging capacitor) where AV, is the voltage across the capacitor when discharge begins (t = 0). The quantity t. time and is called the time constant of the circuit. It describes how long it takes for the capacitor to charge or discharge. RC has dimensions of
Transcribed Image Text:Discharging Capacitor: Kirchoff's loop rule applied to the discharging capacitor circuit gives R > AV: = IR – Δν C loop The current is leaving the positive plate so I = – dQ/dt = -C DAV-//dt. -c dAVc/dt. C Substituting this into loop rule gives a differential equation for Q (t): dVe RC + V = 0 dt This is the simplest differential equation you will learn in your differential equations class. The solution for the differential equation for V.(t) is an exponential: V.(t) = Ve-t/(RC) (discharging capacitor) where AV, is the voltage across the capacitor when discharge begins (t = 0). The quantity t. time and is called the time constant of the circuit. It describes how long it takes for the capacitor to charge or discharge. RC has dimensions of
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