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Chapter 1, Problem 1
How many coulombs are represented by these amounts of electrons:
(a) (b)
17
- 482 × 10
18
- 24 × 10
(c) (d)
19
- 46 × 10
20
- 628 × 10
Chapter 1, Solution 1
(a) q = 6.482x
17 x [-1.602x
(b) q = 1. 24x
18 x [-1.602x
(c) q = 2.46x
19 x [-1.602x
(d) q = 1.628x
20 x [-1.602x
Chapter 1, Problem 2.
Determine the current flowing through an element if the charge flow is given by
(a) q ( ) t = ( 3 t + 8 ) mC
(b) ( ) 8 4 2)C
2 q t = ( t + t-
(c) q( ) t ( 3 e 5 e )nC
-t − 2 t = −
(d) q ( ) t = 10 sin 120 πtpC
(e) ( ) 20 cos 50 t C
4
t q t e
−
Chapter 1, Solution 2
(a) i = dq/dt = 3 mA
(b) i = dq/dt = (16t + 4) A
(c) i = dq/dt = (-3e
-t
-2t ) nA
(d) i=dq/dt = 1200 πcos 120 π t pA
(e) i =dq/dt = − + − e t t 4 t ( 80 cos 50 1000 sin 50 ) μ A
Find the charge q ( t ) flowing through a device if the current is:
(a) i ( ) t = 3 A, q ( ) 0 = 1 C
(b) i ( t )= ( 2 t + 5 )mA, q ( 0 )= 0
(c) i ( t )= 20 cos( 10 t + π / 6 ) μA, q (0)= 2 μC
(d) ( ) 10 sin 40 A, (0) 0
30 = =
− i t e t q
t
Chapter 1, Solution 3
(a) = + =(3t +1) C ∫
q(t) i(t)dt q(0)
(b) (t 5t) mC
2 = + + = + ∫
q(t) (2t s)dt q(v)
(c) q(t) = 20 cos (^) (10t + π/ 6) + q(0) = (2sin(10 t + π/ 6) +1) μC ∫
(d)
e (0.16cos40t 0.12sin40t) C
∫ ( 30 sin 40 t- 40 cost) 900 1600
10 e q(t) 10e sin 40 t q(0)
-30t
Chapter 1, Problem 4.
A current of 3.2 A flows through a conductor. Calculate how much charge passes
through any cross-section of the conductor in 20 seconds.
Chapter 1, Solution 4
q = it = 3.2 x 20 = 64 C
Chapter 1, Problem 5.
Determine the total charge transferred over the time interval of 0 ≤ t ≤ 10s when
1 ( ) 2
i t = t A.
Chapter 1, Solution 5
(^10 )
0
25 C
t q = idt = tdt = = ∫ ∫
The charge flowing in a wire is plotted in Fig. 1.24. Sketch the corresponding
current.
Figure 1.
Chapter 1, Solution 7
25A, 6 t 8
25 A, 0 t 2
dt
dq i
which is sketched below:
The current flowing past a point in a device is shown in Fig. 1.25. Calculate the
total charge through the point.
Figure 1.
Chapter 1, Solution 8
10 1 15 μ C 2
q idt + × =
×
∫
A rechargeable flashlight battery is capable of delivering 85 mA for about 12 h.
How much charge can it release at that rate? If its terminals voltage is 1.2 V, how
much energy can the battery deliver?
Chapter 1, Solution 11
q= it = 85 x
E = pt = ivt = qv = 3672 x1.2 = 4406.4 J
Chapter 1, Problem 12.
If the current flowing through an element is given by
( )
0,t 15s
18 A, 6 t 10s
3 t A, 0 t 6s
it
Plot the charge stored in the element over 0 < t < 20s.
Chapter 1, Solution 12
For 0 < t < 6s, assuming q(0) = 0,
q t idt q tdt t
t t
( ) = + ( ) = + =. ∫ ∫
0 3 0 1 5
0
2
0
At t=6, q(6) = 1.5(6)
2 = 54
For 6 < t < 10s,
q t idt q dt t
t t
( ) = + ( )= + = − ∫ ∫
6 18 54 18 5
6 6
At t=10, q(10) = 180 – 54 = 126
For 10 At t=15, q(15) = -12x15 + 246 = 66
For 15
