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