Introduction to Electric Circuits

166 Nodal and mesh analysis /3 = Is + 12 (7.29) Substituting for ~ from Equation (7.29) in Equation (7.27) we have (R1 + R4)/1- ...

7.4 Mesh current analysis 167 The supermesh equation is therefore RlI 1 + R212 - R213 = _Vsl Now I 1 -- I 2 = Is ~ 11 = Is + 12, ...

168 Nodal and mesh analysis 7.5 SELF-ASSESSMENT TEST 1 Define a matrix. 2 Explain what is meant by a column matrix. 3 Write down ...

(b) Ii1.1 -101 -51 -31 Xlyl - I6~1 7.6 Problems 169 4 Find the determinant ~ the matrix I34 58] 5 Evaluate the determinant of th ...

170 Nodal and mesh analysis 10 Obtain the value of the current flowing through resistor R (- 1 ~) in the circuit of Fig. 7.17 ov ...

7.6 Problems 171 13 Determine the current I supplied by the voltage source in the circuit of Fig. 7.20. 5~ 20mH 10~ --I F----"~" ...

8 Transient analysis 8.1 INTRODUCTION We saw in Chapter 2 that the potential difference across a capacitor cannot change instant ...

8.2 Circuits containing resistance and inductance 173 v( i R L ) ..q[..__.___ VR VL i 0 Figure 8.1 Figure 8.2 ,i...._ r t Applyi ...

174 Transient analysis i.e. it is the steady state value (I) of the current, so we have finally i = 111 - exp (-Rt/L)] (8.2) The ...

8.2 Circuits containing resistance and inductance 175 At t = 0, the rate of change of current is V/L amperes per second and if t ...

176 Transient analysis The sudden disconnection of a d.c. supply v( ) o Figure 8.5 V (a) (b) R i L I ] .~ r-cw'v'~ Suppose that ...

8.2 Circuits containing resistance and inductance 177 Equation (8.9) represents an exponential decay of current, Equation (8.10) ...

178 Transient analysis The response to the application of a pulse Suppose that the pulse of width T seconds (T >i 5r) shown i ...

8.2 Circuits containing resistance and inductance 179 consider the period 0-T (0-40 Ixs). The time constant of the circuit is z ...

180 Transient analysis Example 8.5 Derive the waveforms of the current and the output voltage for the differ- entiator circuit g ...

8.3 Circuits containing resistance and capacitance 181 8.3 CIRCUITS CONTAINING RESISTANCE AND CAPACITANCE The sudden application ...

vt This describes an exponential growth of voltage and is shown in Fig. 8.14. 0.368V Vc 182 Transient analysis 0 T 5T "-t Figure ...

8.3 Circuits containing resistance and capacitance 183 Figure 8.15 0 % 1,' R = V exp (-t/cn) This describes an exponential decay ...

184 Transient analysis The discharge of a capacitor Once the capacitor in Fig. 8.13 has been charged to V volts, it will remain ...

8.3 Circuits containing resistance and capacitance 185 i= vc/R = (V/R)exp (-I/CR) and since V/R = I then i = I exp (-t/CR) (8.20 ...