H5.3b parallel circuits TV3B

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• Middelbare school
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• Leerjaar 3

5.3b Parallel Circuits

Connecting Resistors 

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Last week 

• Current is the same everywhere in series circuit.
  
• The voltage distributes itself among the various components
  
• Equivalent resistances (Req) can be calculated by adding the resistances together. 
• Req =  R₁ + R₂ +..  
  

The LED lamp in the figure burns optimally at a voltage
of 2.0 V. A current of 20 mA flows through the lamp.
The battery supplies a voltage of 9.0 V.
Calculate the value of the resistor that is needed to light
the bulb at the correct voltage.

Elaboration:

Reminder:

Req = R1 + R2 + R3 + .....

Isource = I1 = I2 = I3 =.....

Usource = U1 + U2 + U3....

Given:

U_lamp = 2,0 V

Usource = 9,0 V

I = 20 mA = 0,020 A

Asked:

Rresistor = ?

Conclusion:

Usource = U_lamp + U_resistor

9,0 = 2,0 + U_resistor

U_resistor = 7,0 V

R_resitor        =                                 Ω

​I​​U​​=​0,020​​7,0​​=3,5⋅10​2​​

This lesson

• you know what a parallelcircuit is.
• You can calculate the equivalent resistance of the resistors in a parallel circuit.
• You can calculate the current through each resistor in a parallelcircuit 

Serie circuit

Parallel circuit

Mixed circuit

Parallel

Circuit

Current

• The current distributes itself among the different branches.
• I_tot = I₁ + I₂ + I₃ + ..

parallel

Voltage

• There is the same (source) voltage across each resistor.
• (Because each component is connected directly to the source).
• U_source = U₁ = U₂ = U₃

parallel

• more resistors parallel
• Resistance becomes smaller 
• 1/ R_eq = 1/R₁ + 1/R₂ + ...
  

Equivalent resistance 

parallel

Exercise

Calculate:

- the equivalent resistance

- the total current

1/ R_eq = 1/R₁ + 1/R₂ + ...

R = U / I

Given

R₁ = 10 ohm, R₂ = 40 ohm, U = 4V

Asked

Req en Isource

Formulas

1/ Req = 1/R1 + 1/R2

R = U/I

Elaboration

• 1/Req = 1/10 + 1/40 = 0,125
• Req = 1/0,125 = 8 Ω

• R = 8 ohm, U = 4V
• I_source = U/R = 4/8 = 0,5 A

=

Circuitry Analysis - Parallel

• Step 1: Simplify all parallel 'blocks'.
  
• Step 2: Calculate Req.
  
• Step 3: Calculate Isource.
  
• Step 4: Calculate the voltage across each 'block'.
  
• Step 5: Calculate the individual current through each resistor

Practice 

Step 2:

Req

Step 3:

Isource

Step 4:

U1...

Step 5:

I1....

Reasoning

2 lights are in parallel. Then switch S is opened. 

• What happens with the current through the lamp on the right? (0)
• And through the lamp on the left? (stays same)

Individual assignment

Homework: 2 + 5 t/m 9

Questions? Ask them in the chat or put your mic on.