Here is a combined circuit: a 6.0 Ω and 3.0 Ω parallel pair, in series with a 4.0 Ω resistor. What single resistance does the whole arrangement present to the battery?
The two sub-routines are ones you already run. Check them first:
Find the combined resistance of 10 Ω and 40 Ω in parallel, in Ω.
Resistors of 12 Ω and 18 Ω in series give a total of…
Imagine swapping the whole arrangement for one resistor, chosen so the circuit draws the same current from the source. That one resistance is called the circuit's equivalent resistance. For the parallel pair alone you have called it the combined resistance; the equivalent resistance carries the same idea to the whole circuit.
Run it on the circuit. Stage 1: 1/R = 1/6.0 + 1/3.0 = 0.5, so the pair combines to R = 1/0.5 = 2.0 Ω.
Stage 2: series resistances add. 4.0 Ω + 2.0 Ω = 6.0 Ω. The equivalent resistance of the whole circuit is 6.0 Ω.
Always the pair first. Adding all three resistances, 6.0 + 3.0 + 4.0 = 13 Ω, would treat the parallel branches as series components, and overstate the resistance.
A combined circuit's parallel pair is 30 Ω and 15 Ω. Find the pair's combined resistance, in Ω.
A parallel pair combines to 6.0 Ω, and a 9.0 Ω resistor sits in series with it. Find the equivalent resistance, in Ω.
Find the equivalent resistance of a 12 Ω and 6.0 Ω parallel pair in series with a 5.0 Ω resistor.
Write down the values in the question:
parallel pair: R₁ = 12 Ω, R₂ = 6.0 Ω
series resistor: 5.0 Ω
equivalent resistance = ?
Stage 1: reduce the parallel pair. Write down the equation:
1/R = 1/R₁ + 1/R₂
Substitute in the values:
1/R = 1/12 + 1/6.0
Simplify:
1/R = 0.25
Find R — take the reciprocal of both sides:
R = 4.0 Ω
Stage 2: add the series resistance:
4.0 Ω + 5.0 Ω = 9.0 Ω
The equivalent resistance is 9.0 Ω.
A 7.0 Ω resistor sits in series with a parallel pair of 20 Ω and 30 Ω. Find the equivalent resistance, in Ω.
The 5.0 Ω resistor is swapped for an 8.0 Ω resistor. Find the new equivalent resistance.
Stage 1 is unchanged: the 12 Ω and 6.0 Ω pair still combines to 4.0 Ω.
Stage 2: add the new series resistance:
4.0 Ω + 8.0 Ω = 12 Ω
The equivalent resistance is now 12 Ω.
A 6.0 Ω and 12 Ω parallel pair sits in series with a 10 Ω resistor. Calculate the equivalent resistance of the circuit, in Ω.
A circuit has one parallel pair in series with one resistor. Which is the first step in finding its equivalent resistance?
A 24 Ω and 8.0 Ω parallel pair sits in series with a 5.0 Ω resistor. Calculate the equivalent resistance of the circuit, in Ω.