FAKULTI KEJURUTERAAN ELEKTRONIK DAN KEJURUTERAAN KOMPUTER
BENT 2713- CIRCUIT THEORY 1
TUTORIAL 1
1.
Complete the unit prefix table 1-2, for the following values.
Table 1-2
Units
Powers of 10
Metric Prefix
Symbol
1,000,000,000
109
giga
G
1,000,000
106
mega
M
1,000
103
kilo
k
100
1
.001
10-3
milli
m
.000001
10-6
micro
µ
.000000001
10-9
nano
n
2.
When plugged into a 120 V wall outlet, an electric lamp draws 1.25 A. What it is resistance?
By Ohm’s Law,
𝑽 = 𝑰𝑹
𝐑=
𝑽
𝑰
𝟏𝟐𝟎 𝑽
𝑹 = 𝟏.𝟐𝟓 𝑨 = 𝟗𝟔 Ω
3.
A relay with a coil resistance of 240  requires a minimum of 50 mA to operate. What is the minimum
voltage that will cause it to operate?
Again, by Ohm’s Law,
𝑽 = 𝑰𝑹
𝑽 = 𝟓𝟎 𝒙 𝟏𝟎−𝟑 𝒙 𝟐𝟒𝟎 = 𝟏𝟐 Ω
4.
A 120 V electric coffee maker is rated 960 W. Determine its resistance and rated current.
𝑷 = 𝑽𝑰𝒓𝒂𝒕𝒆𝒅
𝑰𝒓𝒂𝒕𝒆𝒅 =
By Ohm’s Law,
𝑷
𝟗𝟔𝟎 𝑾
=
=𝟖𝑨
𝑽
𝟏𝟐𝟎 𝑽
𝑽 = 𝑰𝑹
𝐑=
𝑽
𝑹=
𝟏𝟐𝟎 𝑽
𝑰
𝟖𝑨
= 𝟏𝟓 Ω
5.
Determine the current flowing through an element if the charge flow is given by:
a) 𝑞(𝑡) = (3𝑡 + 8)𝑚𝐶
b) 𝑞(𝑡) = (8𝑡 2 + 4𝑡 − 2)𝐶
c) 𝑞(𝑡) = (3𝑒 −𝑡 − 5𝑒 −2𝑡 )𝑛𝐶
d) 𝑞(𝑡) = 10𝑠𝑖𝑛120𝜋𝑡 𝑝𝐶
6.
(a) i =
𝑑𝑞
(b) i =
𝑑𝑞
(c) i =
𝑑𝑞
(d) i =
dq
𝑑𝑡
𝑑𝑡
𝑑𝑡
dt
=
𝑑𝑞
=
𝑑𝑞
=
𝑑𝑞
=
dq
(3𝑡 + 8) = 3𝑚𝐴
𝑑𝑡
(8𝑡 2 + 4 − 2𝑡) = 2(8𝑡) + 4 = (16𝑡 + 4)𝑚𝐴
𝑑𝑡
(3𝑒 −𝑡 − 5𝑒 −2𝑡 ) = [−3𝑒 −𝑡 − (−2)(5𝑒 −2𝑡 )]𝑛𝐴 = (−3𝑒 −𝑡 + 10𝑒 −2𝑡 )𝑛𝐴
𝑑𝑡
(10 sin120πt) = [120π(10) cos 120πt] pA = (1200 π cos120πt)pA
dt
Find the charge flowing through a device if the current is:
a) 𝑖(𝑡) = 3𝐴, 𝑞(0) = 1𝐶
b) 𝑖(𝑡) = (2𝑡 + 5)𝑚𝐴, 𝑄(0) = 0
c) 𝑖(𝑡) = 20 𝑐𝑜𝑠(10𝑡 + 𝜋⁄6)𝜇𝐴, 𝑞(0) = 2𝜇𝐶
(a) q(t) = ∫ 𝑖. 𝑑𝑡 = ∫ 3. 𝑑𝑡 = [3𝑡 + 𝑐]
Find c:
t=0, q(0)= 1
q(0)=3(0)+c →
c= 1
q(t) = (3t + 1) C
(b) q(t) = ∫ 𝑖. 𝑑𝑡 = ∫(2𝑡 + 5)𝑑𝑡 = [
2𝑡 2
2
+ 5𝑡 + 𝑐] 𝑚𝐶
Find c:
t=0, q(0)= 0, so c=0
q(t) = (t2 + 5t) mC
𝜋
𝜋
(c) q(t) = ∫ 𝑖. 𝑑𝑡 = ∫[20 cos(10𝑡 + 6 )𝑑𝑡 = 20 ∫ cos (10𝑡 + 6 ) 𝑚𝐶
let u = 10t +
du = 10dt
𝜋
6
Then,
1
𝑑𝑢 = 𝑑𝑡
10
q(t) = ∫
=
20 cos(𝑢)
. du
10
20
∫ cos 𝑢. 𝑑𝑢
10
𝜋
= 2(sin 𝑢) = 2 [sin(10𝑡 + )] + 𝑐
6
Find c:
t=0, q(0)= 2µC
𝜋
q(0) = 2 [sin(10𝑡 + )] + 𝑐
6
180
2µC = 2 [sin(0 +
)] + 𝑐 = (2 sin 300 + 𝑐)µ𝐶
6
2µC = (2 sin 300 + 𝑐)µ𝐶
c = (2 − 1)µ𝐶 = 1µ𝐶
𝜋
q(t) = [2sin(10𝑡 + ) + 1] µC
6
7. If the function f(t) in Figure 1 is the current in amperes entering the positive terminal of an element at
time t (seconds), find:
a) The total charge that has entered between 4 and 9 s,
b) The charge entering at 8 s, and
c) The current at 1, 5 and 8 s.
Take the charge to be 0 at t = 0.
f(t)
8
6
2
0
4
6 7
Figure 1
9
12
t (s)
8. The charge flowing in a wire is plotted in Figure 2 below. Sketch the corresponding current.
Figure 2
9. Figure 3 shows the current through and the voltage across a device.
(a) Sketch the power delivered to the device for t >0
(b) Find the total energy absorbed by the device for the period of 0 < t < 4s.
Figure 3
10.
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 terminal voltage is 1.2 V., how much energy can the battery deliver?
11.
The current entering the positive terminal of a device is 𝑖(𝑡) = 3𝑒 −2𝑡 𝐴, and the voltage across the
device is 𝑣(𝑡) = 5 𝑑𝑖⁄𝑑𝑡 𝑉
a) Find the charge delivered to the device between 𝑡 = 0 and 𝑡 = 2 𝑠
b) Calculate the power absorbed
c) Determine the energy absorbed in 3 𝑠.
12.
Figure 4 shows a circuit with 5 elements. If 𝑝1 = −205 𝑊, 𝑝2 = 60 𝑊, 𝑝4 = 45 𝑊, 𝑝5 = 30 𝑊,
calculate the power 𝑝3 received or delivered by element 3.
Figure 4
13. Consider the circuit of Figure 5. The power consumed by each resistor is as follows: p2(t) = 98 W,
p3(t) = 12 W, p4(t) = 16 W, p5(t) = 768.8 W, and p6(t) = 486 W. The subscript corresponds to the
resistor value.
(a) For each resistor, determine the indicated voltage or current.
(b) Determine the total power delivered by the two sources.
(c) Determine the value of Vin and the value of Iin. Explain your reasoning.
2Ω
+ V2 I3
+ V4 3Ω
Vin
4Ω
I5
5Ω
Figure 5
Iin
6Ω
+
V6
-
14.
Find 𝐼 in the network.
15.
Find 𝑉0 in the circuit
16. Find v and i.
2Ω
2A
3Ω
6V
3Ω
2Ω
+
8V
v
i
17. Find i and vab.
b
a
i
1A
2Ω
5Ω
12 V
3Ω
6Ω
+ 6V 3A
1A
4Ω
18.
A 1.8 kW electric heater takes 15 min to boil a quantity of water. If this is done once a day and power
costs 10 cents/kWh, what is the cost of its operation for 30 days?
19.
An electric stove with 4 burners and an oven is used in preparing a meal as follows:
a) Burner 1 : 20 min
b) Burner 2 : 40 min
c) Burner 3 : 15 min
d) Burner 4 : 45 min
e) Oven : 30 min
If each burner is rated at 1.2 kW and the oven at 1.8kW, and electricity cost 12 cents per kWh,
calculate the cost of electricity used in preparing meal.
20. By referring to Figure 6, find the following:
(a) What is the resistance across the terminals ab of the network shown?
(b) Calculate the voltage across the terminals ac if a 36-V battery is connected across the terminals
ab.
(c) Calculate the power dissipated in the 9-Ω resistor connected across ab and in the 9-Ω resistor
connected across bc of the network when a 36-V source is connected across ab.
9Ω
a
6Ω
c
6Ω
9Ω
9Ω
6Ω
b
Figure 6