Fundamental Electrical and Electronic Principles, Third Edition

250 Fundamental Electrical and Electronic Principlescease. Similarly, when the capacitor has been fully charged, thecharging current will cease.Let us now consider the C-R charging circuit in more detail. Such acircuit is shown in Fig. 8.1 . Let us assume that the capacitor is initiallyfully discharged, i.e. the p.d. between its plates ( v C ) is zero, as will bethe charge, q. Note that the lowercase letters v and q are used because,during the charging sequence, they will have continuously changingvalues, as will the p.d. across the resistor (v R ) and the charging current,i. Thus these quantities are said to have transient values.RCiV RV C‘B’‘A’EFig. 8.1At some time t 0, let the switch be moved from position ‘ A ’ toposition ‘ B ’ . At this instant the charging current will start to flow.Since there will be no opposition offered by capacitor p.d. (v C 0),then only the resistor, R, will offer any opposition. Consequently, theinitial charging current ( I 0 ) will have the maximum possible value forthe circuit. This initial charging current is therefore given by:EI0 Ramp (8.1)Since we are dealing with a series d.c. circuit, then the followingequation must apply at all times:thus, at time t 0E v v volt...............[ 1]RCE v R0i.e. the full emf of E volt is developed across the resistor at the instantthe supply is connected to the circuit. Since v R iR, and at time t 0,i I 0 , this confirms equation (8.1) above.Let us now consider the situation when the capacitor has reached itsfully-charged state. In this case, it will have a p.d. of E volt, a charge ofQ coulomb, and the charging current, i 0. If there is no current flowthen the p.d. across the resistor, v R 0, and eqn [1] is:E 0v C