Introduction to Electric Circuits

46 DC circuit analysis Solution The circuit represents a battery V 1 in parallel with a second battery V2 supplying a load resis ...

3.5 The principle of superposition 47 batteries are in the circuit together is therefore, according to the principle of superpos ...

Figure 3.13 3A 4fi Example 3.5 3.6 THEVENIN'S THEOREM Thevenin, a French engineer, developed work by Helmholtz and published thi ...

Ro Figure 3.15 A IL Rt. 3.6 Thevenin's theorem 49 9 Step 3: to calculate E0 remove the resistor R L in Fig. 3.14 to give the ci ...

[~ 10~ IA T B Figure 3.17 40~ Example 3.6 9 Step 5: put these values for Eo and Ro in the Thevenin equivalent circuit of Fig. 3 ...

3.6 Thevenin's theorem 51 and B at either end of the resistor, r. To calculate E0 we first remove the resistor r in the circuit ...

52 DC circuit analysis I~ = Eo/(Ro + r)- 16.7/(23.33 + r) (3.11) Ie is a maximum when r has its minimum value (i.e. 0 11): & ...

3.7 Norton'stheorem 53 and that V~ = I~ r (3.13) Figure 3.23 ,so I ISC 1 Rsc A lvL To calculate Isc we short circuit the load re ...

54 DC circuit analysis Figure 3.26 [~R1 ~ V2 R3 t i A By current division IL2 = [R~/(R~ + R3)]I2 = [(5/15) X (10/13.33)] = 0.25 ...

3.8 The maximum power transfer theorem 55 Ro A IL RE Figure 3.28 load resistor R L is given by PL -- /L2RL 9 But I L -- Eo/(Ro ...

56 DC circuit analysis transfer theorem tells us (Equation (3.15)) that the power to the load resistor r will be a maximum when ...

3.9 Delta-star transformation 57 and for the resistance between terminals 3 and 1" R3 + R1 = R3,[R,2 + Rz3]/(R12-+- R23 + R3,) ( ...

58 DC circuit analysis Figure 3.32 10~ l t t 5D R31 Ai~l' I :2 l 1 OV R12 7.5D 15s R23 1 --~5~ (RE) Solution This is called a br ...

10 Star-delta transformation 59 (^1) .,, I 1.67s S 5~ i ] ~] I 2.5~ 10V 10~~-] 7.5D. 3 A 1.67~ I --!! L5gZ 10V B Figure 3.34 ...

60 DC circuit analysis and that R12R23//(RI2 + R23 + R31) - R2 we obtain R23 = R2 + R3 + R2R3/R1 (3.28) and R31 = R3 + R1 + R3R1 ...

11 Self-assessment test 61 R23 = R2 + R3 + RzR3/R~ - 5 + 10 + 50/10 = 20 1~ R31 = R 3 + R 1 + R3R1/R 2 = 10 + l0 + 100/5 - 40 ...

62 DC circuit analysis 9 Three resistors each of 12 ~ resistance are connected in delta. Determine the resistance of each of the ...

3.12 Problems 63 Figure 3.42 ,,AIf 1s 6s 4 I |! J A T B 12.[-] 18V 4 In the circuit of Fig. 3.43 the resistor R is variable from ...

64 DC circuit analysis Figure 3.45 1 4V 2V 2V(~+) I I1 O~ ]20~ ~30~ 40~ 7 Three 20 1~ resistors are connected in star and a volt ...

12 Problems 65 between B and C: a resistance of 80 lI between C and D: a resistance of 750 between D and A: a resistance of 10 ...