Chapter 32B - RC Circuits A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University A PowerPoint Presentation.
Presentation on theme: "RC Circuit: Charging Capacitor"— Presentation transcript:
1 RC Circuit: Charging Capacitor VC+-abiInstantaneous charge q on a charging capacitor:At time t = 0: q = CV(1 - 1); q = 0At time t = : q = CV(1 - 0); qmax = CVThe charge q rises from zero initially to its maximum value qmax = CV
2 The time t = RC is known as the time constant. Example 1. What is the charge on a 4-mF capacitor charged by 12-V for a time t = RC?Time, tQmaxqRise in ChargeCapacitort0.63 QR = 1400 WV4 mF+-abiThe time t = RC is known as the time constant.e = 2.718; e-1 = 0.63
3 Example 1 (Cont.) What is the time constant t? Time, tQmaxqRise in ChargeCapacitort0.63 QR = 1400 WV4 mF+-abiThe time t = RC is known as the time constant.In one time constant (5.60 ms in this example), the charge rises to 63% of its maximum value (CV).t = (1400 W)(4 mF)t = 5.60 ms
4 RC Circuit: Decay of Current VC+-abiAs charge q rises, the current i will decay.Current decay as a capacitor is charged:
5 The current is a maximum of I = V/R when t = 0. Current DecayRVC+-abiTime, tIiCurrent DecayCapacitort0.37 IConsider i when t = 0 and t = .The current is a maximum of I = V/R when t = 0.The current is zero when t = (because the back emf from C is equal to V).
6 The time t = RC is known as the time constant. Example 2. What is the current i after one time constant (t = RC)? Given R and C as before.R = 1400 WV4 mF+-abiTime, tICurrent DecayCapacitort0.37 IThe time t = RC is known as the time constant.e = 2.718; e-1 = 0.37
7 Charge and Current During the Charging of a Capacitor. Time, tQmaxqRise in ChargeCapacitort0.63 ITime, tIiCurrent DecayCapacitort0.37 IIn a time t of one time constant, the charge q rises to 63% of its maximum, while the current i decays to 37% of its maximum value.
8 RC Circuit: Discharge C C After C is fully charged, we turn switch to b, allowing it to discharge.RVC+-abRVC+-abiDischarging capacitor. . . loop rule gives:Negative because of decreasing I.
9 Discharging Capacitor VC+-abiNote qo = CV and the instantaneous current is: dq/dt.Current i for a discharging capacitor.
10 From definition of logarithm: Prob. 45. How many time constants are needed for a capacitor to reach 99% of final charge?RVC+-abiLet x = t/RC, then:e-x = or e-x = 0.01From definition of logarithm:4.61 time constantsx = 4.61
11 Prob. 46. Find time constant, qmax, and time to reach a charge of 16 mC if V = 12 V and C = 4 mF. +-abi1.4 MWC12 Vt = RC = (1.4 MW)(1.8 mF)t = 2.52 sqmax = CV = (1.8 mF)(12 V);qmax = 21.6 mCContinued . . .
12 From definition of logarithm: Prob. 46. Find time constant, qmax, and time to reach a charge of 16 mC if V = 12 V and C = 4 mF.RV1.8 mF+-abi1.4 MWC12 VLet x = t/RC, then:From definition of logarithm:x = 1.35Time to reach 16 mC:t = 3.40 s