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

1.8 Summation notation 49
thecircuitwhenwritingdowntheequations.Ifthearrowisinthedirectionoftravel
then it is given a positive sign; if it opposes the direction of travel it is given a
negative sign.
The equations are
V b
V a
V d
V d
V c
V e
V c
V a
V b
V e
V a
−V b
−V c
=0 V a
−V b
−V d
−V e
=0 V c
−V d
−V e
=0
If the equations are solved and the voltage has a negative sign it indicates that the
polarityisoppositetothedirectionofthevoltagearrowdrawnonthediagram.KVL
and KCL are the fundamental circuit laws that allow networks of electronic components
to be mathematically analysed. Although they are simple in concept they are
very powerful techniques.
EXERCISES1.8
1 Writeoutfullywhatismeantbyeachofthefollowing
expressions:
(a) ∑ 4
k=1 x k
(c) ∑ 7
k=1 x k
(b) ∑ 4
i=1 x i
(d) ∑ 3
k=1 x 2 k
(e) ∑ 4
j=1 (x j −2) 3 (f) ∑ 3
n=0 (2n +1) 2
4 Determine the current,I,at eachofthe following
circuitnodes:
(a)
3 A
I
1 A
(b)
3 A
I
1 A
2 Writeoutfully
(a) ∑ 4
k=1 (−1) k k (b) ∑ 5
k=1 (−1) k+1 k 2
3 Writethe followingsums more concisely byusing
sigma notation:
(c)
3 A
I
1 A
(d)
I 1
I 2
I 3
I
(a) 1 3 +2 3 +3 3 +···+10 3
1
(b)
1 − 1 2 + 1 3 − 1 4 +···− 1 12
(c) 1+ 1 3 + 1 5 + 1 7