Combination Circuits

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Combination Circuits
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• Steps to Solve Combined Series-Parallel Circuits
• 1. If necessary, draw a diagram of the circuit.
• 2. Find any parallel resistors in the circuit
  and simplify them into one equivalent resistance
  using the formula for parallel equivalent
  resistance.
• 3. If necessary, draw a new diagram using the
  equivalent resistor instead of the multiple
  previous resistors.
• 4. Find any resistors that are now in series
  and replace them with the equivalent resistance
  using the formula for series equivalent
  resistance.
• 5. If necessary, draw a new diagram using the
  equivalent resistance.
• 6. Once the circuit is reduced into a single
  resistor, you can now solve for the current using
  Ohms Law.

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• Calculate the following
• total equivalent resistance
• total current
• the current across each resistor
• the voltage drop across each resistor

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Draw the Circuit
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Solve for Req for parallel resistors

• 1/Req 1/4 1/12
• 1/Req .333
• Req 3 O

Remember, the first step in combination circuits
is ALWAYS to calculate the equivalent resistance
of the parallel resistors!
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Redraw the Circuit
5 O
24 V
3 O
8 O
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Solve for Req for series resistors

• Req 8 3 5
• Req 16 O

Note the 3O resistor came from the result of our
solving for the Req for the parallel circuit
section
5 O
24 V
3 O
8 O
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Redraw the Circuit
24 V
16 O
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Solve for the Total Current

• Vt (It)(Rt)
• 24 It(16)
• It 1.5 amps

Ohms Law V IR
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Solve for the Current through Each Resistor

• Since resistors R1 and R4 are in series, the
  current in series-connected resistors is the same
  everywhere. Therefore,
  
  
• It I1 I4 1.5 amps

Note In a Series Circuit, to solve for total
current It I1 I2 I3
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Solving for the Current through Each Resistor

• Since resistors R2 and R3 are in parallel, the
  current in parallel-connected resistors is added
  up to equal the total current. Therefore,
  
  
• It I1 I4 1.5 amps

However, this gets a bit tricky because the
resistors do not have the same value therefore
we must first calculate the voltage drop through
each resistor and then come back to calculate the
current
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• Calculate the voltage drop across the
  series-connected resistors. (R1 and R4 in
  diagram)
• V1 I1R1 V4
  I4R4
• V1 (1.5)(5) 7.5 V V4 (1.5)(8)
  12 V

Series Circuit, to solve for total voltage Vt
V1 V2 V3
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• Next, subtract the values for the series voltage
  from the total voltage
• VT Vseries Vparallel 24
  V 7.5 V 12 V 4.5 V

This tells us that the voltage drop across EACH
parallel resistor is 4.5 V because Vt V1 V2
V3
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• Lastly, using Ohms Law calculate the current
  traveling through each parallel resistor
• V2 I2R2
  V3 I3R3
• 4.5 I2(4)
  4.5 I3(12)
• I2 1.125 amps I3
  .375 amps

Remember, current varies through each parallel
resistor since there is more than one path for
the electrons to take!
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Results of our calculations