Download Circuits II - Uplift North Hills Prep

Resistors in Series
• All the current must follow the same path.
• Each component has the same current going
through it
•
If current is disrupted through one element (e.g. the light goes out)
then they all go out.
Resistors in Series
• All the current must follow the same path.
• Each component has the same current going
through it
•
If current is disrupted through one element (e.g. the light goes out)
then they all go out.
Equivalent or total or effective resistance is the one that
could replace all resistors resulting in the same current.
Req = R1+ R2 + R3
Adding more resistors in series increases equivalent
resistance!
Resistors in Parallel
•
Current can branch to multiple paths
• Current varies through each resistor (greater
resistance = smaller current).
• The current flowing into a node equals the
current that flows out of that node
I = I1 + I2 + I3 .
• The voltage drop across each resistor is the
same.
•
Each device is independent; if one resistor goes out, the others keep
working.
Resistors in Parallel
•
Current can branch to multiple paths
• Current varies through each resistor (greater
resistance = smaller current).
• The current flowing into a node equals the
current that flows out of that node
I = I1 + I2 + I3 .
• The voltage drop across each resistor is the
same.
•
Each device is independent; if one resistor goes out, the others keep
working.
1
1
1
1
=
+
+
Req R1 R2 R3
equivalent resistance
is smaller than the
smallest resistance.
We do: Calculating Req
We do: Calculating Req
Req = R1 + R2 = 8 Ω + 8 Ω = 16 Ω
1
𝑅𝑒𝑞
=
1
𝑅1
+
Req = 4 Ω
1
𝑅2
=
1
8Ω
+
1
8Ω
=
1
4Ω
We do: Calculating Req
We do: Calculating Req
You do: Calculating Req
You do: Calculating Req
Calculating Current, Potential Drop, and
Power Dissipated
• To calculate current through a circuit, find the Req for all resistors
in a circuit, then use Ohm’s Law (I = V/R)
Example: What is the current through this circuit?
Calculating Current, Potential Drop, and
Power Dissipated
• To calculate current through a circuit, find the Req for all resistors
in a circuit, then use Ohm’s Law (I = V/R)
Example: What is the current through this circuit?
I = 60V / 10Ω = 6A
Calculating Current, Potential Drop, and
Power Dissipated
To find potential drop across a resistor:
1. find overall current
2. Use Ohm’s Law to find voltage drop
*Note: the voltage drop of EACH parallel resistor is equal to the
voltage drop across the equivalent resistor
Calculating Current, Potential Drop, and
Power Dissipated
To find potential drop across a resistor:
1. find overall current
2. Use Ohm’s Law to find voltage drop
*Note: the voltage drop of EACH parallel resistor is equal to the
voltage drop across the equivalent resistor
Example: What is the voltage drop across each resistor?
1st: Find Req for all resistors
2nd: Find I
3rd: Calculate V = IR for each resistor,
remembering to use Req for the two parallel
resistors
Calculating Current, Potential Drop, and
Power Dissipated
To find potential drop across a resistor:
1. find overall current
2. Use Ohm’s Law to find voltage drop
*Note: the voltage drop of EACH parallel resistor is equal to the
voltage drop across the equivalent resistor
Example: What is the voltage drop across each resistor?
1st: Find Req for all resistors
Req = 5Ω + 3Ω + 8Ω = 16Ω
2nd: Find I
I = 24 V / 16Ω = 1.5 A
3rd: Find voltage drop across each resistor:
V1 = 5Ω* 1.5A = 7.5 V
V2 = V3 = 3Ω* 1.5A = 4.5 V
V4 = 8Ω* 1.5A = 12 V
Calculating Current, Potential Drop, and
Power Dissipated
To find potential drop across a resistor:
1. find overall current
2. Use Ohm’s Law to find voltage drop
*Note: the voltage drop of EACH parallel resistor is equal to the
voltage drop across the equivalent resistor
Example: What is the voltage drop across each resistor?
Check your work! The sum of all voltage drops
should equal the emf.
7.5V + 4.5V + 12V = 12V
3rd: Find voltage drop across each resistor:
V1 = 5Ω* 1.5A = 7.5 V
V2 = V3 = 3Ω* 1.5A = 4.5 V
V4 = 8Ω* 1.5A = 12 V
Calculating Current, Potential Drop, and
Power Dissipated
Remember that current divides up at a node. More current will go
through the path with lesser resistance.
To find current across parallel resistors …
1) Find the total current in a circuit
2) Find the voltage drop across the parallel resistors
3) Use Ohm’s Law
Calculating Current, Potential Drop, and
Power Dissipated
Remember that current divides up at a node. More current will go
through the path with lesser resistance.
To find current across parallel resistors …
1) Find the total current in a circuit
2) Find the voltage drop across the parallel resistors
3) Use Ohm’s Law
Example: What is the current across R2 and R3?
1) We already found that Itotal =1.5 amps
2) We already found that Vparallel = 3 V
3) I2 = 4.5 V / 4Ω = 1.125 A
I3 = 4.5 V / 12 Ω = 0.375 A
Check your work! Remember:
Itotal = I2 + I3 = 1.5 amps!
Calculating Current, Potential Drop, and
Power Dissipated
To find power dissipated across each resistor –
1) Calculate the voltage drop across each resistor
2) Calculate current through each resistor
3) Use the power law (P = IV)
Example: What is the power dissipated through each
resistor?
1)
2)
3)
4)
P1 = IV = 1.5 A * 7.5 V = 11.25 W = 10 W
P2 = IV = 1.125 A * 4.5 V = 5.06 W = 5 W
P3 = IV = 0.375A * 4.5 V = 1.69 W = 2 W
P4 = IV = 1.5A * 12V = 18 W = 20 W
Example
Example