1) A 6-V battery is connected to an RC circuit (R = 16 ? and C = 4.1 ?F). If the

Question

1) A 6-V battery is connected to an RC circuit (R = 16 ? and C = 4.1 ?F). If the capacitor is initially uncharged, what is the current in the circuit immediately after the connection is made?

2) A 10-V battery is connected to an RC circuit (R = 6 ? and C = 6 ?F). Initially, the capacitor is uncharged. What is the final charge on the capacitor (in ?C)?

3) The quantity t1/2=? ln 2 is called the half-life of an exponential decay, where ?=RC is the time constant in an RC circuit. The current in a discharging RC circuit drops by half whenever t increases by t1/2. For a circuit with R=2 k? and C=3 ?F, if the current is 6 mA at t=5 ms, at what time (in ms) will the current be 3 mA?

Explanation / Answer

1. apply time consatnt of RC ckt as T = Rc

T = 16 * 4.1 e-6

T = 6.56 *10^-5 secs

part A:

as just the ckt is on,

Intitial current i = 0 -------------<<<<<<<<<<<<<<<<-answer to part A

---------------

part B :

inital charge Qi = CV

Qi =- 6e -6 * 10 = 60 uC

final charge Q f =   Qi *(1-e^-t/Rc)

Qf = 60 uC *(1-e^-t/T)      ( after one time constnat)

Qf = 0.632 * 60 uC

Qf =   21.72 uC -------------<<<<<<<<<<<<<<<<-answer to part B
---------------------------

opart C:

use

I = io e^ -t/Rc

e^-t/RC = 3/6 = 0.5

-t/RC   =   ln (0.5)

-t/RC = -0.693

t = 0.693 * 2000 * 3e-6

t = 4.158 mSecs -------------<<<<<<<<<<<<<<<<-answer to part C

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.