Study Guide
Resistors in Series and Parallel
-
University:
Kentucky State University -
Course:
PHY 212 | General Physics II Academic year:
2024
-
Views:
440
Pages:
36
Author:
Adowj7b
Resistors in Circuits Vs Capacitors in Circuits
Different elements, yet same logic!
Two simple ways to connect resistors
Series:
Parallel:
A
B
A
B
Circuit elements can be connected neither in series nor in parallel.
Check out examples 4 & 9 Identifying series and parallel connections
A
B
If you can move your finger along the wires from A to B
without passing a junction, i.e., without ever having a
choice of which wire to follow, the components are connected
in series. In contrast:
A
???
B
If you ever have a choice of which wire to follow when
moving from A to B, the circuit elements are not in series.
In other words, the elements are not connected in series
because of the existence of the junction.
Do not jump to conclusions!
If each element provides an alternative path between
the same points A and B, the elements are in parallel. Are these resistors in series or parallel?
+ -
V
parallel
Not enough information: It matters where you put the source of emf. Are these resistors in series or parallel?
+
V
series Resistors in series
R1
A
V1
I
R2
I
R3
B
V2
I
V3
I
+ -
V
Current:
same current flows through all resistors
(conservation of charge: all charge entering the series
of resistors at A must leave it at B)
Unless we have leakage somewhere!
Voltage:
voltages in a series add up VAB=V1+V2+V3
(Recall capacitors’ lecture. Conservation of energy) Equivalent resistance
R1
A
V1
I
R2
I
Req
R3
B
I
V2
V
V3
I
I
V
+ -
+ -
Replace the series combination by a single “equivalent” resistor
(producing same total voltage for same current)
V = V1 + V2 + V3
V = IR1 + IR2 + IR3
IR1 + IR2 + IR3 = IReq
R1 + R2 + R3 = Req
V = IReq Generalize this to any number of resistors:
R eq R i
i
resistances in series add up!
Req in series and Ceq in parallel are Additive
Note: for resistors in series, Req is always greater than any of the Ri. Resistors in parallel
Current:
• current I splits into currents I1, I2, I3
I = I1+ I2+ I3 (conservation of charge)
I1
R1
V
I2
A
R2
V
Voltage:
• Voltage drops across all three
resistors are identical
VAB= V1= V2= V3 (conservation of energy)
I3
R3
V
I
+ V
B Equivalent resistance
I1
R1
Req
A
V
I2
A
R2
V
I3
R3
V
I
V
+ -
I = I 1 + I2 + I3
V
V
V
I= + +
R1 R 2 R 3
B
V
I=
R eq
I
V
+ -
Replace parallel combination by single
equivalent resistor
V
V
V
V
= + +
R eq R1 R 2 R 3
Dividing both sides by V gives
1
1
1
1
= + +
R eq R1 R 2 R 3
B Generalize this to any number of resistors:
1
1
R eq
i Ri
• for resistors in parallel, the inverse resistances add
Note: for resistors in parallel, Req is always less than any of the Ri. Summary:
Series
B
A
i
same I, V’s add
Parallel
A
same V, I’s add
R eq R i
B
1
1
R eq
i Ri Example 4 : calculate the equivalent resistance of the resistor
“ladder” shown. All resistors have the same resistance R.
A
B
Recall: Circuit elements can be connected neither in series nor in parallel. Where to start?
Series
A
B • new color indicates an equivalent resistor made up of
several original ones
Parallel
A
B Series
A
B Parallel
A
B Series
A
B All done!
A
B Example 5 : For the circuit below, calculate the current drawn
from the battery and the current in the 6 resistor.
10
8
6
8
1
3
9V
Hmm… I wish if it’s feasible to work out the example on
the whiteboard in a class room! One more time: where to start? What’s your strategy?
10
8
6
8
1
3
9V
Replace parallel combination (green) by its equivalent. 10
4
6
3
1
9V
Replace the series combination (blue box) by its equivalent. 10
10
1
3
9V
Replace the parallel combination (orange) by its equivalent.
We are left with an equivalent circuit of 3 resistors in series,
which is easy handle. Now perform the actual calculation a step at a time.
R1=10
R3 and R4 are in parallel.
R3=8
R2=6
R4=8
R5=
3
1
1
1
1 1 2 1
= +
= + = =
R 34 R 3 R 4 8 8 8 4
R 34 = 4
R6=1 =9 V
R1=10
R2 and R34 are in series.
R2=6
R34=4
R6=1 =9 V
R5=
3
R 234 = R 2 +R 34 = 6 + 4 =10 Let’s shrink the diagram a bit, and work this a step at a time.
R1=10
R1 and R234 are in parallel.
1
R234=10
R5=
3
R1234
1
1
1
1
2 1
= +
= + =
=
R1 R 234 10 10 10 5
R1234 = 5
R6=1 =9 V
R1234, R5 and R6 are in series.
R1234=5
R5=
3
R6=1 =9 V
R eq = R1234 +R5 +R 6 =5+3+1
R eq = 9 Calculate the current drawn from the battery.
R eq = 9
R1234=5
R5=
3
I=1 A
R6=1 =9 V
V =IR
9
I=
= =1 A
R eq 9
Quiz: Which is larger: the current in R6=1 or in R5= 3 ?
The currents in R6=1 , R5= 3 , and R1234=5 are equal. Find the current in the 6 resistor.
R1=10
R3=8
R2=6
I=1 A
R4=8
R5=
3
There are many ways to
do the calculation. This is
just one.
R6=1 =9 V
R1=10
R234=10
I=1 A
R6=1 =9 V
R5=
3
V1 = V234 = V1234 (parallel). Find the current in the 6 resistor.
I
V1234 = I R1234 = (1)(5) = 5 V
R1234=5
R5=
3
I=1 A
V1 = V234 = 5 V
R6=1 =9 V
R1=10
V234 = I234 R234
I234
R234=10
I=1 A
R6=1 =9 V
R5=
3
I234 = V234 / R234 = 5/10
I234 = 0.5 A Find the current in the 6 resistor.
R1=10
R3=8
I2=I234
R2=6
I=1 A
R4=8
R6=1 =9 V
I234 = I2 = I34 = 0.5 A
R5=
3
I2 = 0.5 A Example 6 : two 100 light bulbs are connected
(a) in series (right) and (b) in parallel (left) to a 24 V battery.
For which circuit will the bulbs be brighter?
The upshot is that the more power “consumed,” the brighter the
bulb. In other words, we use power as a proxy for brightness. Example: two 100 light bulbs are connected (a) in series and (b) in
parallel to a 24 V battery. What are the current & the voltage through
each bulb? For which circuit will the bulbs be brighter?
(a) Series combination.
R1
100
+ -
Req = R1 + R2
I
V = I Req
V = I (R1 + R2)
R2
100
V = 24 V
Quiz: V1? V2? 12 V
Recall: V = I(R + r) of Example 1
I = V / (R1 + R2) = 24 V / (100 + 100 ) = 0.12 A Example: two 100 light bulbs are connected (a) in series and (b) in
parallel to a 24 V battery. What are the current & the voltage through
each bulb? For which circuit will the bulbs be brighter?
(b) Parallel combination.
1
1
1
1
1
2
=
+
=
+
=
R eq
R1
R2
100
100 100
I1
V
I2
V = I R eq I = V
24
= 0.48 A
50
I1 = I2 = I
R2
V
R eq = 50
I =
R1
2
+ -
R eq
just because R1= R2
= 0.24 A
I
V = 24 V
I Example: two 100 light bulbs are connected (a) in series and (b) in
parallel to a 24 V battery. What are the current & the voltage through
each bulb? For which circuit will the bulbs be brighter?
(a) Series combination.
for each bulb:
P=
I2R
P = (0.12 A)2 (100 )
P = 1.44 W
R1
100
R2
100
+ -
I
V = 24 V
We could have used
P = IV = (0.12 A) (12 V)
or
P = V2 / R = (12 V)2 / ( 100 ) Example: two 100 light bulbs are connected (a) in series and (b) in
parallel to a 24 V battery. What are the current & the voltage through
each bulb? For which circuit will the bulbs be brighter?
(b) Parallel combination.
I1
R1
V
for each bulb:
P = V2 / R
P = (24 V)2 / ( 100 )
I2
I
R2
V
I
+ -
V = 24 V
P = 5.76 W
We also know each current, so we could have used P = I2R. Example: two 100 light bulbs are connected (a) in
series (left) and (b) in parallel (right) to a 24 V battery.
For which circuit will the bulbs be brighter?
I1
R1
100
R2
100
+ -
I
V = 24 V
R1
V
I2
I
R2
V
+ -
V = 24 V
Compare:
Pseries = 1.44 W
Pparallel = 5.76 W
The bulbs in parallel are brighter
I This is what you see if you connect 40 W bulbs directly to
a 120 V outlet.
DO NOT TRY AT HOME especially with the fact that you are
“enjoying” the midnight curfew!!
Off
On
Related Documents
- Step Graded Diode
- Assignment 2: Q and A
- Sequential Circuit - Study Note
- Latch (Temporary Storage of Bits)
- Set-Reset Flip-Flop
- Delay Flip Flop
- Linear Graded Diode
- Zener Diode Reference Materials
- Subtractor Class Notes
- Half Adder Course Materials
- Photo Diode Tutorial Notes
- Practical Diode Circuit
- Gases Practice Test
- Full Adder CKT
- Types of Clock Pulse
- T-Flip Flop
- J-K Flip Flop - Physic Note
- K-Map Tutorial Notes
- Universal Logic Gate
- Boolean Theorem, Distributive Law, Demorgan's Law and Transposition Theorem
Resistors in Series and Parallel
of 36
Recommended Documents
⏰ Deadline pressure?
Get your assignment done in just 3 hours. Quick, easy, and available 24/7.
Report
Tell us what’s wrong with it:
Thanks, got it!
We will moderate it soon!
Free up your schedule!
Our EduBirdie Experts Are Here for You 24/7! Just fill out a form and let us know how we can assist you.
Take 5 seconds to unlock
Enter your email below and get instant access to your document