082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

50 Chapter 1 Review of algebraic techniques
5 FindV a in each ofthe followingcircuits:
(a)
6 FindV a andV b usingKVL.
1 V
1 V
2 V
3 V
V a
1 V
V a
V b
(b)
−1 V
2 V
V a
Solutions
1 (a) x 1 +x 2 +x 3 +x 4 (b)x 1 +x 2 +x 3 +x 4
(c) x 1 +x 2 +x 3 +x 4 +x 5 +x 6 +x 7
(d) x 2 1 +x2 2 +x2 3
(e) (x 1 −2) 3 + (x 2 −2) 3 + (x 3 −2) 3 + (x 4 −2) 3
(f) 1+3 2 +5 2 +7 2
2 (a) −1+2−3+4
(b) 1−4+9−16+25
∑
3 (a) 10
k=1 k 3
(b)
(c)
∑ 12 (−1) k+1
k=1 k
∑ 3n=0 1
2n+1 or ∑ 4 1
n=1 2n−1
4 Allsolved usingKCL
(a) 3−1−I=0 · · · I = 2
(b) 3+1−I=0 · · · I = 4
(c) 3+1+I=0 · · · I=−4
(d) I 1 +I 2 +I 3 −I=0, · · · I=I 1 +I 2 +I 3
orI= ∑ 3
k=1 I k
5 Both solved usingKVL
(a) 2−1−V a =0 · · ·Va =1
(b) 2+(−1) +V a =0 · · ·Va =−1
6 3−1−V a =0 · · ·Va =2
3−1−1−V b =0 · ·Vb =1
orV a −1−V b =0 · · · by substitution forV a ,
V b =1
REVIEWEXERCISES1
1 Simplify eachofthe followingasfar aspossible: 2 Simplify asfar aspossible:
(a) 7 6 7 4 6 3
(b)
6 −2 (c) (3 4 ) −2 (a) x 7 x −3 (b) (x 2 ) 4 (c)
√
(d) 3 4 6 2 (e) (3 2/3 4 1/3 ) 6 (f) 10−3
10 −4 (d) (y −2 ) −1 (e) y 1/3 yy 2
(√ ) −1 x
x