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Resistors in
Series/Parallel
HOW WE WIRE THE CIRCUITS
Series vs Parallel Circuits
Series Circuit
Electrons only have one
path to flow through.
Parallel Circuit
There are MULTIPLE paths for
the current to flow through.
RESISTORS IN SERIES
Series Circuits
Series Circuit
When electrons have to flow through one part to get to the next part
◦ More components = more resistance
◦ Increase resistance = decrease current (flow)
◦ Less current = less bright bulbs
◦ As voltage increases, current increases
Series Circuit – Pros & Cons
Problems with Series:
The more devices (resistors) in a series circuit, the less current
passes through (dimmer bulbs).
If one resistor breaks (a bulb goes out) the entire series is
turned off.
Series Circuit – Current is the same
• The total charge through each resistor per unit time, Q1 ,
Q2 and Q3 are the same, based on conservation of charge.
𝑸 𝟏 = 𝑸 𝟐 = 𝑸 𝟑
𝑸 𝟏
𝒕
=
𝑸 𝟐
𝒕
=
𝑸 𝟑
𝒕
• The current stays the same in
electric components in the same
path connecting in series, based
on conservation of charges.
Ieq = I1 = I2 = I3
Series Circuit
Potential Difference/Voltage Drop
• Based on conservation of energy: charges gain
energy/potential, and then deliver energy/potential to each
resistor/component.
Veq = V1+V2+ V3
• According to Ohm’s Law V= IR
• Ieq Req = I1 R1+ I2 R2+ I3 R3…
• Since Ieq = I1 = I2 = I3 = I
I Req = IR1+ IR2+ IR3
Total Resistance = Sum of all resistors in the series
Req = R1+R2+ R3
Series Circuit - Current
Current = amount of charge (flow of electrons)
◦ Like the flow of water, A current can't just disappear (appear)
◦ Since only one path if some electrons flow through R1, then they have to
continue flowing through R2 and R3.
◦ Since the Current is the same through the entire circuit
◦ IT=I1=I2=I3
Series Circuit - Voltage
Voltage is the electric equivalent of water pressure.
◦ The higher the voltage, the faster electrons will flow through the
conductor.
Each component has resistance that causes a drop in voltage
(reduction in voltage).
Total Voltage = The sum of voltages across each
series resistors
VT = V1 + V2 + V3…
Series vs Parallel Chart
Series Parallel
Voltage (V) Vtot = V1 + V2 + V3…
Current (I) Itot=I1=I2=I3
Resistance (R) Req = R1+R2+ R3…
Series Circuit - Example
• Given
– Vbattery = 12 V
– R1 = 50 W,
R2 = 100 W,,
R3 = 100 W
What is the equivalent
resistance of the circuit load?
Resistors in Parallel
Parallel Circuit – Pros and Cons
Advantages
The more resistors in parallel connection, the less total
resistance the circuit load has.
If one resistor breaks (a bulb goes out) the rest on other
routes do not.
Problems
The more resistors in parallel connection, the higher total
current the circuit load has.
Which is better? Series or Parallel?
Parallel
Most things are wired in parallel for household items.
When there are too many items in parallel, the current
increases and energy would be drawn and dissipated faster.
Of course, this also increases the risk of fire
This is why homes have fuses or circuit breakers. They
turn off everything in the circuit when current moves too
fast.
TollBooth Explanation
Adding toll booths in series increases
resistance and slows the current flow.
Adding toll booths in parallel lowers
resistance and increases the current flow.
Parallel Circuits
Parallel Circuit - Current
ALL paths are used!
◦ The charge divides up into all branches; Currant slits at the junction
◦ One branch can have more current than another branch (depends on
resistance in branch).
Total current = sum of current in each path
IT = I1 + I2 + I3…
Parallel Circuit - Voltage
• A charge only passes through a single resistor.
• Voltage/energy carried by each charge drops across the
resistor
• In the following circuit, each loop has one resistor. Each
charge gains energy from the battery and delivers energy
to each resistor. So that, each resistor in each loop gains
the same energy/potential
• Total voltage = the voltage across each individual resistor
VT = V1 = V2 = …
Parallel Circuit - Resistance
• The total current IT = I1 + I2 + I3…
• Apply Ohm’s Law:
𝑽 𝑻
𝑹 𝑻
=
𝑽 𝟏
𝑹 𝟏
+
𝑽 𝟐
𝑹 𝟐
+
𝑽 𝟑
𝑹 𝟑
Total voltage = the voltage across each
individual resistor VT = V1 = V2= V3…
𝑽
𝑹 𝑻
=
𝑽
𝑹 𝟏
+
𝑽
𝑹 𝟐
+
𝑽
𝑹 𝟑
𝟏
𝑹 𝑻
=
𝟏
𝑹 𝟏
+
𝟏
𝑹 𝟐
+
𝟏
𝑹 𝟑
𝑹 𝑻 = (
𝟏
𝑹 𝟏
+
𝟏
𝑹 𝟐
+
𝟏
𝑹 𝟑
)
−𝟏
Series vs Parallel Chart
Series Parallel
Voltage (V) Vtot = V1 + V2 + V3… Vtot = V1 = V2 = …
Current (I) Itot=I1=I2=I3 Itot = I1 + I2 + …
Resistance (R) Req = R1+R2+ R3… 1/Req=1/R1+1/R2+1/R3
Parallel Circuit - Example
• Given
– Vbattery = 12 V
– R1 = 50 W, R2 = 100 W, R3 = 100 W
Determine the equivalent
resistance of the circuit load.

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17 3-1 resistors in series and parallel circuits 2020

  • 2. Series vs Parallel Circuits Series Circuit Electrons only have one path to flow through. Parallel Circuit There are MULTIPLE paths for the current to flow through.
  • 5. Series Circuit When electrons have to flow through one part to get to the next part ◦ More components = more resistance ◦ Increase resistance = decrease current (flow) ◦ Less current = less bright bulbs ◦ As voltage increases, current increases
  • 6. Series Circuit – Pros & Cons Problems with Series: The more devices (resistors) in a series circuit, the less current passes through (dimmer bulbs). If one resistor breaks (a bulb goes out) the entire series is turned off.
  • 7. Series Circuit – Current is the same • The total charge through each resistor per unit time, Q1 , Q2 and Q3 are the same, based on conservation of charge. 𝑸 𝟏 = 𝑸 𝟐 = 𝑸 𝟑 𝑸 𝟏 𝒕 = 𝑸 𝟐 𝒕 = 𝑸 𝟑 𝒕 • The current stays the same in electric components in the same path connecting in series, based on conservation of charges. Ieq = I1 = I2 = I3
  • 8. Series Circuit Potential Difference/Voltage Drop • Based on conservation of energy: charges gain energy/potential, and then deliver energy/potential to each resistor/component. Veq = V1+V2+ V3 • According to Ohm’s Law V= IR • Ieq Req = I1 R1+ I2 R2+ I3 R3… • Since Ieq = I1 = I2 = I3 = I I Req = IR1+ IR2+ IR3 Total Resistance = Sum of all resistors in the series Req = R1+R2+ R3
  • 9. Series Circuit - Current Current = amount of charge (flow of electrons) ◦ Like the flow of water, A current can't just disappear (appear) ◦ Since only one path if some electrons flow through R1, then they have to continue flowing through R2 and R3. ◦ Since the Current is the same through the entire circuit ◦ IT=I1=I2=I3
  • 10. Series Circuit - Voltage Voltage is the electric equivalent of water pressure. ◦ The higher the voltage, the faster electrons will flow through the conductor. Each component has resistance that causes a drop in voltage (reduction in voltage). Total Voltage = The sum of voltages across each series resistors VT = V1 + V2 + V3…
  • 11. Series vs Parallel Chart Series Parallel Voltage (V) Vtot = V1 + V2 + V3… Current (I) Itot=I1=I2=I3 Resistance (R) Req = R1+R2+ R3…
  • 12. Series Circuit - Example • Given – Vbattery = 12 V – R1 = 50 W, R2 = 100 W,, R3 = 100 W What is the equivalent resistance of the circuit load?
  • 14. Parallel Circuit – Pros and Cons Advantages The more resistors in parallel connection, the less total resistance the circuit load has. If one resistor breaks (a bulb goes out) the rest on other routes do not. Problems The more resistors in parallel connection, the higher total current the circuit load has.
  • 15. Which is better? Series or Parallel? Parallel Most things are wired in parallel for household items. When there are too many items in parallel, the current increases and energy would be drawn and dissipated faster. Of course, this also increases the risk of fire This is why homes have fuses or circuit breakers. They turn off everything in the circuit when current moves too fast.
  • 16. TollBooth Explanation Adding toll booths in series increases resistance and slows the current flow. Adding toll booths in parallel lowers resistance and increases the current flow.
  • 18. Parallel Circuit - Current ALL paths are used! ◦ The charge divides up into all branches; Currant slits at the junction ◦ One branch can have more current than another branch (depends on resistance in branch). Total current = sum of current in each path IT = I1 + I2 + I3…
  • 19. Parallel Circuit - Voltage • A charge only passes through a single resistor. • Voltage/energy carried by each charge drops across the resistor • In the following circuit, each loop has one resistor. Each charge gains energy from the battery and delivers energy to each resistor. So that, each resistor in each loop gains the same energy/potential • Total voltage = the voltage across each individual resistor VT = V1 = V2 = …
  • 20. Parallel Circuit - Resistance • The total current IT = I1 + I2 + I3… • Apply Ohm’s Law: 𝑽 𝑻 𝑹 𝑻 = 𝑽 𝟏 𝑹 𝟏 + 𝑽 𝟐 𝑹 𝟐 + 𝑽 𝟑 𝑹 𝟑 Total voltage = the voltage across each individual resistor VT = V1 = V2= V3… 𝑽 𝑹 𝑻 = 𝑽 𝑹 𝟏 + 𝑽 𝑹 𝟐 + 𝑽 𝑹 𝟑 𝟏 𝑹 𝑻 = 𝟏 𝑹 𝟏 + 𝟏 𝑹 𝟐 + 𝟏 𝑹 𝟑 𝑹 𝑻 = ( 𝟏 𝑹 𝟏 + 𝟏 𝑹 𝟐 + 𝟏 𝑹 𝟑 ) −𝟏
  • 21. Series vs Parallel Chart Series Parallel Voltage (V) Vtot = V1 + V2 + V3… Vtot = V1 = V2 = … Current (I) Itot=I1=I2=I3 Itot = I1 + I2 + … Resistance (R) Req = R1+R2+ R3… 1/Req=1/R1+1/R2+1/R3
  • 22. Parallel Circuit - Example • Given – Vbattery = 12 V – R1 = 50 W, R2 = 100 W, R3 = 100 W Determine the equivalent resistance of the circuit load.