Transcript D.C. Circuits_2 - GTU e

EEE (2110005) - ACTIVE LEARNING ASSIGNMENT
Presented by: Divyang Vadhvana(130120116086)
Branch: Information Technology
Electrical circuits often contain one or more
resistors grouped together and attached to
an energy source, such as a battery.
The following symbols are often used:
Ground
+ - + - + - + -
Battery
+
-
Resistor
Resistors are said to be connected in series
when there is a single path for the current.
I
R1
VT
R2
R3
Only one current
For series
connections:
The current I is the same for
each resistor R1, R2 and R3.
The energy gained through E
is lost through R1, R2 and R3.
The same is true for voltages:
I = I1 = I2 = I3
VT = V1 + V2 + V3
The equivalent resistance Re of a number of
resistors connected in series is equal to the
sum of the individual resistances.
VT = V1 + V2 + V3 ; (V = IR)
I
R1
VT
R2
R3
Equivalent Resistance
ITRe = I1R1+ I2R2 + I3R3
But . . . IT = I1 = I2 = I3
Re = R1 + R2 + R3
The output direction from a
source of emf is from + side:
-
a
+ b
E
Thus, from a to b the potential increases by E;
From b to a, the potential decreases by E.
A
R
AB: V = +9 V – 3 V = +6 V
3V
BA: V = +3 V - 9 V = -6 V
B
-
9V
+
+
Example: Find V for path AB
and then for path BA.
Consider the simple series circuit drawn below:
D
A
-
2
C
-
15 V
+
+
4
3V
B
Path ABCD: Energy and V
increase through the 15-V
source and decrease
through the 3-V source.

E
=
1
5
V
-3
V
=
1
2
V
The net gain in potential is lost through the two
resistors: these voltage drops are IR2 and IR4,
so that the sum is zero for the entire loop.
R2
Resistance Rule: Re = R
C
u
r
r
e
n
t:
Voltage Rule:

E
I

R
E = IR
R1
E2
E1
A complex circuit is one
containing more than a
single loop and different
current paths.
At junctions m and n:
I1 = I2 + I3 or I2 + I3 = I1
Junction Rule:
I (enter) = I (leaving)
I3
R3
R1
m
E2
n
I1
R2
E1
I2
Resistors are said to be connected in parallel
when there is more than one path for current.
Parallel Connection:
2
4
6
Series Connection:
2
4
6
For Parallel Resistors:
V2 = V4 = V6 = VT
I2 + I 4 + I 6 = I T
For Series Resistors:
I2 = I 4 = I 6 = I T
V2 + V4 + V6 = VT
VT = V 1 = V 2 = V 3
IT = I1 + I2 + I3
VT
Parallel Connection:
R1
V
Ohm’s law: I 
R
V
V
T
1 V
2 V
  3
R
R
e
1 R
2 R
3
R2
R3
1 1 1 1
  
R
R
e
1 R
2 R
3
The equivalent resistance
for Parallel resistors:
1 N 1

Re i1 Ri
The equivalent resistance Re for two parallel
resistors is the product divided by the sum.
1 1 1
  ;
R
R
R
e
1
2
Example:
VT
R1
6
R2
3
RR
Re  1 2
R1 R2
(3
)(6
)
R
e
3
6
Re = 2 
In complex circuits resistors are often connected
in both series and parallel.
R
1
In such cases, it’s best to
use rules for series and
parallel resistances to
reduce the circuit to a
simple circuit containing
one source of emf and
one equivalent resistance.
VT R2
VT
R3
Re
Kirchoff’s first law: The sum of the currents
entering a junction is equal to the sum of the
currents leaving that junction.
Junction Rule: I (enter) = I (leaving)
Kirchoff’s second law: The sum of the emf’s
around any closed loop must equal the sum
of the IR drops around that same loop.
Voltage Rule:
E = IR
 When applying Kirchoff’s laws you must
assume a consistent, positive tracing direction.
 When applying the voltage rule, emf’s are
positive if normal output direction of the emf is
with the assumed tracing direction.
 If tracing from A to B, this
emf is considered positive.
 If tracing from B to A, this
emf is considered negative.
A
E
+
A
E
+
B
B
 When applying the voltage rule, IR drops are
positive if the assumed current direction is
with the assumed tracing direction.
 If tracing from A to B, this
IR drop is positive.
 If tracing from B to A, this
IR drop is negative.
A
I
+
A
I
+
B
B
1. Assume possible consistent
flow of currents.
2. Indicate positive output
R1
directions for emf’s.
3. Indicate consistent tracing
direction. (clockwise)
Junction Rule: I2 = I1 + I3
Voltage Rule: E = IR
E1 + E2 = I1R1 + I2R2
+
I1
Loop I
E2
R3
E1
R2
I2
I3
E3
4. Voltage rule for Loop II:
Assume counterclockwise
positive tracing direction.
Voltage Rule: E = IR
Bottom Loop (II)
R1
Yes! - E2 - E3 = -I2R2 - I3R3
Loop I
R3
E1
R2
E2
E2 + E3 = I2R2 + I3R3
Would the same equation
apply if traced clockwise?
I1
I2
I3
Loop II
+
E3
5. Voltage rule for Loop III:
Assume counterclockwise
positive tracing direction.
+
Voltage Rule: E = IR
Outer Loop (III)
R1
Yes!
E3 - E1 = I1R1 - I3R3
Loop I
R3
E1
R2
E2
E3 – E1 = -I1R1 + I3R3
Would the same equation
apply if traced clockwise?
I1
I2
I3
Loop II
+
E3
6. Thus, we now have four
independent equations
from Kirchoff’s laws:
+
I2 = I 1 + I 3
Outer Loop (III)
R1
I1
Loop I
R2
E2
E1 + E2 = I1R1 + I2R2
E2 + E3 = I2R2 + I3R3
E3 - E1 = -I1R1 + I3R3
R3
E1
I2
I3
Loop II
+
E3
Rules for a simple, single loop circuit
containing a source of emf and resistors.
Resistance Rule: Re = R
C
u
r
r
e
n
t:

E
I

R
E = IR
Single Loop
-
2
3
3V
C
-
A
18 V
+
+
Voltage Rule:
D
B
For resistors connected in series:
For series
connections:
I = I1 = I2 = I3
VT = V1 + V2 + V3
Re = R1 + R2 + R3
Re = R
2
3 1
12 V
Resistors connected in parallel:
V = V1 = V2 = V3
IT = I1 + I2 + I3
For parallel
connections:
1 N 1

Re i1 Ri
RR
Re  1 2
R1 R2
Parallel Connection
R1
R2
R3
VT
2
12 V
4
6
Kirchoff’s first law: The sum of the currents
entering a junction is equal to the sum of the
currents leaving that junction.
Junction Rule: I (enter) = I (leaving)
Kirchoff’s second law: The sum of the emf’s
around any closed loop must equal the sum
of the IR drops around that same loop.
Voltage Rule:
E = IR