The last lesson's circuit gets its battery: a 12 V supply drives the 4.0 Ω resistor in series with the 6.0 Ω and 3.0 Ω parallel pair. How much current does the battery supply?
The routine ends with one Ohm's-law step. Check the equation first:
A 30 Ω resistor has 6.0 V across it. Enter the current in A.
Step 1: find the equivalent resistance of the whole circuit. You found it in the last lesson: the pair combines to 2.0 Ω, and 4.0 Ω + 2.0 Ω = 6.0 Ω.
Step 2: treat the circuit as its equivalent: one 6.0 Ω resistor across 12 V.
Apply I = V/R: I = 12/6.0 = 2.0 A. The battery supplies 2.0 A.
The supply current is the only current this routine finds. How the 2.0 A divides between the 6.0 Ω and 3.0 Ω branches is a different question, and this lesson does not need it.
Run the sense check: 12 V across the 4.0 Ω resistor alone would drive 3.0 A. The rest of the circuit adds resistance, so the real supply current must be smaller. And 2.0 A is.
Now the routine on a fresh circuit, one step per question: a 30 V battery drives a 3.0 Ω resistor in series with a 36 Ω and 12 Ω parallel pair.
A combined circuit's parallel pair is 36 Ω and 12 Ω. Find the pair's combined resistance, in Ω.
A 3.0 Ω resistor sits in series with a parallel pair of 36 Ω and 12 Ω. Find the circuit's equivalent resistance, in Ω.
An 18 V battery drives a 2.0 Ω resistor in series with a 12 Ω and 6.0 Ω parallel pair. Calculate the current the battery supplies.
Write down the values in the question:
V = 18 V
series resistor: 2.0 Ω
parallel pair: 12 Ω and 6.0 Ω
I = ?
Step 1: find the equivalent resistance. Reduce the pair:
1/R = 1/12 + 1/6.0 = 0.25
R = 1/0.25 = 4.0 Ω
Add the series resistance:
equivalent resistance = 2.0 Ω + 4.0 Ω = 6.0 Ω
Step 2: write down the equation:
I = V/R
Substitute in the values:
I = 18/6.0
Simplify:
I = 3.0 A
The battery supplies 3.0 A.
A 30 V battery drives a 3.0 Ω resistor in series with a 36 Ω and 12 Ω parallel pair. What current does the battery supply, in A?
The 18 V battery is swapped for a 24 V battery, with the resistors unchanged. What current does the battery supply now?
The equivalent resistance is unchanged: 6.0 Ω.
Write down the equation:
I = V/R
Substitute in the values:
I = 24/6.0
Simplify:
I = 4.0 A
The battery now supplies 4.0 A.
A 50 V supply drives a 7.0 Ω resistor in series with a 30 Ω and 45 Ω parallel pair. Calculate the current the supply delivers, in A.
To find the current a battery supplies to a combined circuit, what must be found first?
A student finds a combined circuit's supply current by dividing the source voltage by the sum of all three resistances. Why is the student's current too small?