Page 197 - WCS - Electrical

WORKSHOP CALCULATION & SCIENCE - CITS

24
Therefore R  24 ohms = 2.4 ohms
ohms = 2.4 ohms
Therefore R 
10

ohms = 2.4 ohms
Therefore R  24 10
Example 10
Example
Example
Two resistors of 2 and 4 ohms are switched in parallel
Two resistors of 2 and 4 ohms are switched in parallel
to a 6V battery
Two resistors of 2 and 4 ohms are switched in parallel
to a 6V battery
to a 6V battery
– Calculate the total resistance
– Calculate the total resistance
– Calculate the total resistance
– Find the total current and partial current.
– Find the total current and partial current.
– Find the total current and partial current.
Parallel connection
In a parallel connection the beginning and the ends of the loads are connected together.
Features of parallel connection:
The total resistance of a parallel connection is always
• • The current flowing through each load depends upon the resistance of the load.
Solution
•
The total resistance of a parallel connection is always
The total resistance of a parallel connection is always
• smaller than the smallest resistance in the circuit. Solution
smaller than the smallest resistance in the circuit.
Solution
• The voltage across each load is the same and is equal to the voltage applied to the circuit.
smaller than the smallest resistance in the circuit.
• In parallel connection the reciprocal of the total Total resistance
Total resistance
•
In parallel connection the reciprocal of the total
• The total resistance of a parallel connection is always smaller than the smallest resistance in the circuit.
resistance is equal to the sum of the reciprocals of all
Total resistance
In parallel connection the reciprocal of the total
•
resistance is equal to the sum of the reciprocals of all
1
1
1
resistances in the circuit.
1
resistance is equal to the sum of the reciprocals of all
1
=
1 +
• In parallel connection the reciprocal of the total resistance is equal to the sum of the reciprocals of all resistances
resistances in the circuit.
+
=
resistances in the circuit.
R
R 2
l in the circuit. + ... R tot 1 R 1 1 R 1 R 2
= l + l
= l + l + ...
= tot
+ 1
l
1
2
l = l + l + ... + ...
1
l
= l + l
+
V = V = V 2 2 1 2 2 = R 1 tot 1 1 = R +2 1 2 4 = R 1 2 2 + 1
1 ...
+
=
V = V = V ...
1
1 4
+
1
2
1 1
1
V = V = V ... 2 1 = = 3 2 + Ω 2 4 3 = 4 4 4
V = V = V ...
1 1
1 1
1
2
1
1
2






..........



1
R 1  R  .......... = 4 3 = Ω 4 Ω
1
R
R
 RR
..........



1
2
1
=
R
R R 2 R tot 4 R 4 = = 4 1 1 = Ω 1 Ω
1
Example 1 2 tot 3 4 3 3 1 Ω 3
Example
Example R tot = 3 = 1 3
Example
Two resistances of 4 ohms and 6 ohms are connected in I Total = I + I current
Two resistances of 4 ohms and 6 ohms are connected in
I Total = I + I current
Two resistances of 4 ohms and 6 ohms are connected in parallel. Determine the total resistance.
2
1
parallel. Determine the total resistance. I Total = I + I current
2
1
Two resistances of 4 ohms and 6 ohms are connected in
parallel. Determine the total resistance.
6V
2
parallel. Determine the total resistance. But I But I U 1 R = 1 U = 2Ω = 6V 3A = 3A
=
1
1
1
1
=
1
1
1



6V 2Ω
U R
1



=
(since parallel connection)
R 1   (since parallel connection) But I 1 U R 1 6V 2Ω = 3A
=

1
(since parallel connection)
1
1
R
R
R
R
R


(since parallel connection)
1
R  21 2 I 2 = I 2 R = = U 4Ω = = 6V 1.5A 1.5A
R
R
=
1 2 1 10 I 2 = 2 U R = 2 6V 4Ω 1.5A
=
1
1

Therefore
1
1

10
R



Therefore 1 1  I total I total 2 1.5A + 4Ω 1.5A

3A =




+
3A =

Therefore
1

10
1 24
6
4
6

1.5A
total
+
Therefore R R  4R 4  24 4.5= 3A = Amp Amp
I
24
4.5=

6

Therefore R = ohms = 2.4 ohms
Therefore R  24 ohms = 2.4 ohms 4.5= Amp
10
Example
Assignment
Example
Assignment
Two resistors of 2 and 4 ohms are switched in parallel to a 6V battery
Assignment
Two resistors of 2 and 4 ohms are switched in parallel
– Calculate the total resistance
1 to a 6V battery R = 12 ohms 3 3 V = 220 v
V = 220 v
R = 12 ohms
1
1
1
V = 220 v
– Find the total current and partial current.
1
R = 12 ohms
R = 40 ohms
– Calculate the total resistance R = 22 ohms 3 R = 40 ohms
1 R = 22 ohms
1
2
1
2
R = 40 ohms
R = 22 ohms
R = 24 ohms in series
1 V = 100 v
2 R = 24 ohms in series
1
– Find the total current and partial current. V = 100 v
3
1
3
V = 100 v
R = 24 ohms in series
R = ______ ohms (in series) R 2
1 (in series) R
3 R = ______ ohms
= ______ ohms
R = ______ ohms (in series) R 2 2
= ______ ohms
2 2 R = 15 ohms = ______ ohms
R = 15 ohms
1
1
2 R = 25 ohms 4 4 V = 80 v
V = 80 v
R = 15 ohms
1 R = 25 ohms
2
= 2 A
2
= 2 A
I
R = 25 ohms
V = 220 v 184 4 I V = 80 v
2 V = 220 v
= 2 A
R = 30 ohms
V = ______ v I R = 30 ohms
V = 220 v
CITS : WCS - Electrical - Exercise 18
1
1
1 V = ______ v (in series)
R = 30 ohms
1
1 (in series)
V = ______ v
1 V = ______ v
• The total resistance of a parallel connection is always Solution V = ______ v R = ______ ohms
2
(in series)
R = ______ ohms
2
2
smaller than the smallest resistance in the circuit. V = ______ v R = ______ ohms
2
2
• In parallel connection the reciprocal of the total Total resistance 2
resistance is equal to the sum of the reciprocals of all
resistances in the circuit. 1 = 1 + 1
R R R Workshop Calculation & Science : (NSQF) Exercise 1.7.34 105
Workshop Calculation & Science : (NSQF) Exercise 1.7.34
l = l + l + ... tot 1 1 2 + 1 2 Workshop Calculation & Science : (NSQF) Exercise 1.7.34 105 105
1
2
1
V = V = V ... = 2 + 4 = 4
1
2
1  1  = 3 Ω
1

..........


R R R 4
1 2 4 1
R = = 1 Ω
Example tot 3 3
Two resistances of 4 ohms and 6 ohms are connected in I Total = I + I current
parallel. Determine the total resistance. 1 2
U 6V
1   But I 1 = R 1 = 2Ω = 3A
1
1


R R R (since parallel connection)
1 2 = U = 6V = 1.5A
I 2 R 4Ω
1 1 1 10 2



1.5A
Therefore  I total 3A = +
R 4 6 24
4.5= Amp
Assignment
1 R = 12 ohms 3 V = 220 v
1
R = 22 ohms R = 40 ohms
2 1
R = 24 ohms in series V = 100 v
3 1
R = ______ ohms (in series) R 2
= ______ ohms
2 R = 15 ohms
1
R = 25 ohms 4 V = 80 v
2
V = 220 v I = 2 A
V = ______ v R = 30 ohms
1
1 (in series)
V = ______ v
2 R = ______ ohms
2
Workshop Calculation & Science : (NSQF) Exercise 1.7.34 105