Transcript CombinationCircuits

Combination Circuits
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 Ohm’s Law.
Calculate the following:
a)total equivalent
resistance
b)total current
c)the current across each
resistor
d)the voltage drop across
each resistor
Draw the Circuit
Solve for Req for parallel resistors
Remember, the first
step in combination
circuits is ALWAYS to
calculate the
equivalent resistance
of the parallel
resistors!
1/Req = 1/4 + 1/12
1/Req = .333
Req = 3 Ω
Redraw the Circuit
5Ω
24 V
3Ω
8Ω
Solve for Req for series resistors
Req = 8 + 3 + 5
Req = 16 Ω
Note: the 3Ω
resistor came from
the result of our
solving for the Req
for the parallel
circuit section
5Ω
24 V
3Ω
8Ω
Redraw the Circuit
24 V
16 Ω
Solve for the Total Current
Ohm’s Law:
V = IR
Vt = (It)(Rt)
24 = It(16)
It = 1.5 amps
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 =…
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
Series Circuit, to solve for total voltage: Vt = V1 + V2 + V3 +…
Calculate the voltage drop across the seriesconnected resistors. (R1 and R4 in diagram)
V1 = I1R1
V1 = (1.5)(5) = 7.5 V
V4 = I4R4
V4 = (1.5)(8) = 12 V
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 = …
Lastly, using Ohm’s Law calculate the current
traveling through each parallel resistor
V2 = I2R2
4.5 = I2(4)
I2 = 1.125 amps
Remember, current
varies through each
parallel resistor since
there is more than
one path for the
electrons to take!
V3 = I3R3
4.5 = I3(12)
I3 = .375 amps
Results of our calculations: