Download 6-1 SERIES CIRCUITS INTRODUCTION An electric circuit has a

SERIES CIRCUITS
INTRODUCTION
An electric circuit has a complete path through which electrons can flow from the negative terminal of the
voltage source, through the connecting wires, through the load and back to the positive side of the voltage
source.
In any type of work that involves electricity, knowledge of the types of circuits is desirable. The purpose of this
lesson is to provide you with an understanding of series connected voltages and resistances.
After completing this lesson you will be able to:
1.
Correctly identify a series circuit.
2.
Compute unknown values of voltage, current, resistance and power.
3.
Mathematically convert metric values to base equivalents and base values to base equivalents.
6-1
1.
SERIES CONNECTED VOLTAGES
As mentioned before, each electric circuit requires a voltage source. One source for a direct current circuit
is a cell or battery. The arrangement of the cells in a circuit depends on the load requirements of voltage
and current. If the voltage must be high, cells are connected in series.
a.
Connecting Cells in Series
The voltage of a single primary cell, commonly called a dry cell, is 1.5 volts. When the voltage
required by a load is higher than 1.5 volts it is necessary to use more than one cell and the cells
must be connected in series. A of Figure 1 shows four 1.5 volt dry cells connected in series. The
negative terminal of the first cell is connected to the positive terminal of the second cell, the negative
terminal of the second cell is connected to the positive terminal of the third cell, and the negative
terminal of the third cell is connected to the positive terminal of the fourth cell. The positive
terminal of the first cell and the negative terminal of the fourth cell are free and become the output
terminals for the circuit. B of Figure 1 is a schematic drawing of the four cells in series. The long
vertical line represents the negative terminal of each cell. When cells are connected in series the
same amount of current flows through each cell. The total voltage of the cells connected in series is
equal to the sum of the voltages of the individual cells.
A.
1.5 v
1.5 v
1.5 v
1.5 v
6.0 v
B.
FIGURE 1 - SERIES VOLTAGE CONNECTION
b.
Effect of Series Voltages
According to Ohm’s Law, current in an electric circuit is directly proportional to the voltage of the
circuit. If the resistance is kept constant and the voltage is increase, the current will increase in
proportion to the increase in voltage. The opposite is also true. If the voltage is decreased, the
current will also decrease. These circuits are alike in that they have a voltage source connected to a
6-ohm resistor. There is only one path for current to flow. The difference in the four circuits (figure
2) is in the value of the applied voltage that is obtained from dry cells, each of which furnishes 1.5
volts.
6-2
+
+
E1 = 1.5v
+
E = 1.5 v
+
R=6
+
_
_
E2 = 1.5 v
I = .25 a
_
Er = 3 v
I = .5 a
(A)
(B)
Et = 3 v
+
+
E1 = 1.5v
E1 = 1.5 v
+
+
+
R=6
E2 = 1.5 v
_
+
_
_
Er = 4.5 v
E2 = 1.5 v
+
Er = 6 v
+
_
E4 = 1.5 v
I = .75 a
(C)
R=6
_
E3 = 1.5 v
E3 = 1.5 v
+
I=1a
Et = 4.5 v
(D)
Et = 6 v
FIGURE 2 - EFFECT OF SERIES VOLTAGES
2.
SERIES CONNECTED RESISTANCES
As mentioned before, each electric circuit will have some type of load. The load may be a resistor, a lamp,
a heater, a motor or any other type of appliance. Each of these devices offers opposition to the flow of
current - resistance.
a.
Connecting Resistances in Series
A of Figure 3 shows three 3-ohm resistors connected in series. The conductor connects the resistors
from end to end. When resistors are connected in series, the same current flows through each
resistor. B of Figure 3 is a schematic drawing of the three resistors in series. The resistor symbol
may also be used in simple schematic diagrams to represent any resistance rather than the symbol of
the actual component.
6-3
3 OHMS
3 OHMS
R1=3
3 OHMS
R3=3
R2=3
FIGURE 3 - SERIES RESISTANCE CONNECTION
b.
Effect of Changing Resistance
According to Ohm’s Law, the current in an electric circuit is inversely proportional to the resistance
of the circuit. If the voltage is kept constant and the resistance is increased, the current will decrease.
The opposite is also true, if resistance is decreased, the current will increase. The circuits in Figure 4
are alike in that they have a 6-volts source connected to a resistance. The difference in the four
circuits is in the number of resistances connected in series.
+
+
_
+
R1 = 2
Er1 = 3 v
+
R=2
E=6v
E=6v
Er = 6 v
I = 1.5a
_
_
I=3a
_
R2 = 2
Er2 = 3 v
_
(A)
(B)
+
+
E=6v
_
I=1a
_
(C)
Rt = 4
_
+
R1 = 2
Er1 = 2 v
_
+
R1 = 2
Er1 = 1.5v
+
R2 = 2
Er2 = 2 v
R3 = 2
Er3 = 2 v
_
_
+
Rt = 6
+
E=6v
_
I = .75 a
R4 = 2
Er4 = 1.5 v
_
+
+
(D)
FIGURE 4 - EFFECT OF CHANGING RESISTANCE
6-4
+
Rt = 8
_
R2 = 2
Er2 = 1.5 v
R3 = 2
Er3 = 1.5 v
3.
ANALYSIS OF A SERIES CIRCUIT
If a circuit is designed so that current flow has only one possible path, the circuit is called a series circuit.
By carefully tracing the connections of each battery, resistance and conductor, it can be determined that the
total current must flow through each device . In analyzing a series circuit, Ohm’s Law, the power formula
and laws for series circuits are used as required . The laws for series circuits should be learned.
a.
Laws for Voltage
(1) In a series circuit, the total voltage is equal to the sum of the individual voltage sources.
Et = E 1 + E 2 + E 3
(2) In a series circuit, the sum of the voltage drops across the individual resistances is equal to
the total voltage.
Et = Erl + Er2 + Er3
b.
Law for Resistance
In a series circuit, the total resistance is equal to the sum of the individual resistances.
Rt = R1 + R2 + R3
c.
Law for Current
In a series circuit, the same amount of current flows in all parts of the circuit and is equal to the total
voltage (Et) divided by the total resistance (Rt).
I=
d.
Et
Rt
Laws for Power
(1) In a series circuit, the total power consumed is equal to the power consumed by the individual
resistance.
Pt = Prl + Pr2 +Pr3
(2) In a series circuit, the total power supplied is equal to the sum of the power supplied by the
individual voltage sources.
Pt = P1 + P2 + P3
SUMMARY
A series circuit is one which has only one path for current to flow, so the same amount of current flows in
all parts of the circuit. The voltage of batteries connected in series adds together. The resistance of load
connected in series also adds together. Likewise, the power consumed by the individual resistances adds
together. Ohm’s Law and the power formula will apply at each individual component and also to the circuit
as a whole.
STUDENT PRACTICAL EXERCISE
6-5
LESSON:
1.
Series Circuits
______________
_______
12v
_________________
Et = _____________
12v
2.
Et = _____________
3.5 v
3.5 v
3.5 v
3.
Rt = _____________
2 ohms
3 ohms
4.
2 ohms
2 ohms
Et = _____________
It = _____________
12 v
Rt = _____________
Pt = _____________
12 v
2 ohms
5.
1.5 ohms
1.5 ohms
Et = _____________
It = _____________
6v
Rt = _____________
1.5 ohms
6v
Pt = _____________
6v
R3 = 3 ohms
6.
Et = _____________
6-6
36v
R2 = 5 ohms
It = _____________
Rt = _____________
R1 = 10 ohms
Pt = _____________
R1 = 10 ohms
Et = _____________
I = 2a
7.
R2 = 15ohms
It = _____________
Rt = _____________
R3 = 5 ohms
Pt = _____________
R3 = 3
Et = _____________
I = 4.5 a
8.
ohms
R2 = 6 ohms
It = _____________
Rt = _____________
R1 = 11 ohms
Pt = _____________
R1 = 30 ohms
Et = _____________
I = 10a
9.
R2 = 20 ohms
It = _____________
Rt = _____________
Pt = _____________
R3 = 10 ohms
10.
R3 = 6 ohms
6-7
Et = _____________
24v
11.
It = _____________
R2 = 3 ohms
Rt = _____________
R1 = 1 ohm
Pt = _____________
R3 = 3 ohms
Et = _____________
R2 = 3 ohms
48v
It = _____________
Rt = _____________
12.
R1 = 4 ohms
Pt = _____________
R3 = 50 ohms
Et = _____________
60v
It = _____________
R2 = 10 ohms
Rt = _____________
R1 = 20 ohms
Pt = _____________
R3 = 4 ohms
Et = _____________
I = 10a
13.
It = _____________
R2 = 6 ohms
Rt = _____________
R1 = 20 ohms
14.
R3 = 10 ohms
Pt = _____________
Et_____
6-8
Er3 = 20v
R2 = 10 ohms
Er2 = 20v
R1 = 10 ohms
Er1 = 20v
It_____
Rt_____ R1_____ R2______ R2_____
Pt_____
30v
15.
R1 = 5 ohms
R2 = 10 ohms
R3 = 5 ohms
6-9
Et_____
It_____
Rt_____ R1_____ R2______ R2_____
Pt_____