Combination Circuits
What is a combination circuit?
Combination or compound circuits contain both series and parallel connections.
Crucial that we understand the differences between series and parallel circuits.
1st: Find total resistance. Ex.1
2nd: Apply Ohm’s law
With the Rtotal = 2Ω + 2Ω + 6Ω
Rtotal = 10Ω Determine the total current in the circuit
by using Ohm’s law.∆Vtotal = 12V Req = 10Ω
∆V =IR Itot = ∆V/R Itot = 12V/10Ω Itot = 1.2A
3rd: Determine the current values.(at each resistor)
Resistor 1 and 4 are in Series, so Itot = I1 = I4 = 1.2 A
For parallel branches, the sum of the current in each individual branch is equal to the current outside the branches. So,
I2 = I3 = 0.6 A
4th: Determine the voltage drop.
Now that the current at each individual resistor location is known, use Ohm's law to determine the voltage drop across each resistor.V1 = I1 • R1 = (1.2A) • (2Ω) = 2.4VV2 = I2 • R2 = (0.6A) • (4Ω) = 2.4V V3 = I3 • R3 = (0.6A) • (4Ω) = 2.4V V4 = I4 • R4 = (1.2A) • (6Ω) = 7.2V
Example 2.
1st: Find total resistance.
For the parallel part:1 / Req = 1/(4Ω) + 1/(12Ω)Req = 3.00Ω
For the total circuit.Rtot = R1 + Req + R4 = 5Ω + 3Ω+ 8ΩRtot = 16 Ω
2nd: Apply Ohm’s law
Itot = Vtot / Rtot = (24V) / (16Ω)Itot = 1.5 Amp
Resistors R1 and R4 are in series so,Itot = I1 = I4 = 1.5 Amp
Resistors R2 and R3 are parallel, this means
I2 + I3 = 1.5 Amp.
3rd Determine the voltage drop.
In our last example, R2 and R3 were the same.
To determine the voltage drop R2 and R3, the voltage drop across the two series-connected resistors (R1 and R4) must first be determined. V1 = I1• R1 = (1.5A)•(5 ): V1 = 7.5 V
V4 = I4• R4 = (1.5A)•(8 ): V4 = 12 V
4th Determine the missing current values.
We know, Vtot = 24V and the 19.5V was consumed by R1 and R4. So,
V2 = V3 = 4.5 V Apply Ohm’s law to determine the
current at R2 and R3. I2 = V2/R2 = (4.5V)/(4Ω): I2 = 1.125 A I3 = V3/R3 = (4.5V)/(12Ω): I3 = 0.375 A
Solution.
Homework.
Pg. 728 # 36 & 37