Series and Parallel Circuits
Unit 3: Electricity and Electronics. Lesson 12 of 53 in BMET Academy.
There are only two ways to connect two parts: one after the other, or side by side. Every circuit you meet is a mix of those two, called a combination circuit, and each of the two has its own set of rules.
Series: one path
Parts in series sit in a single loop, so the current has nowhere else to go.
- Current is the same everywhere in the loop.
- Voltage divides between the parts, and the drops add up to the source.
- Resistance adds: R total = R1 + R2 + R3. That total is the equivalent resistance, the single resistor that would behave the same way.
- One part opening stops everything.
Example: 9 V with 220 ohm and 470 ohm in series. Total resistance is 690 ohm, so the current is 9 / 690 = 0.013 A. Across the 220 ohm that is 0.013 x 220 = 2.87 V; across the 470 ohm, 0.013 x 470 = 6.13 V. The two drops add to 9.0 V, the source. The bigger resistor always takes the bigger share.
That last rule is why a fuse goes in series: when it opens, everything downstream stops. It is also why an old string of holiday lights wired in series went completely dark when a single bulb failed.
Parallel: more than one path
Parts in parallel are connected across the same two points, so each one sees the whole voltage.
- Voltage is the same across every branch.
- Current divides, and the branch currents add up to the total.
- Resistance total is less than the smallest branch. For exactly two parallel resistors, use product over sum: (R1 x R2) / (R1 + R2).
- One branch opening leaves the others working.
Example: 9 V across 220 ohm and 470 ohm in parallel. The 220 ohm branch draws 9 / 220 = 0.041 A and the 470 ohm branch draws 9 / 470 = 0.019 A, so the feed carries 0.060 A. Total resistance is 9 / 0.060 = 150 ohm, which is indeed below 220. Product over sum agrees: (220 x 470) / 690 = 150 ohm.
The voltage divider
Two resistors in series across a supply give you a smaller voltage at the point between them, in proportion to the resistances. In the example above, the junction sits 6.13 V above the bottom of the 470 ohm resistor. Circuit boards use dividers everywhere to scale a signal down to something a chip can read, and a drifting divider is a classic cause of a reading that is wrong by a steady percentage.
Why the hospital is wired in parallel
Every outlet in a room is connected across the same supply, so each one gets the full 120 V and unplugging one device does not kill the others. The same is true inside a device: the boards, the display, and the pump motor hang in parallel off the power supply, each drawing the current it needs at the same voltage. If outlets were in series, a single unplugged pump would darken the ward.
In the lab you build both circuits, measure the two series drops and add them, then measure both branch currents and the feed, and watch the branch currents add up. Seeing it on the display is what makes it stick.
This lesson includes an interactive lab in the course.
Series and Parallel Circuits, explained slowly
The two topologies, side by side
Series Parallel path one loop, no branches two or more branches current the same in every part divides; branch currents add to the total voltage divides; drops add to the source same across every branch resistance R total = R1 + R2 + R3 less than the smallest branch two resistors just add them (R1 x R2) / (R1 + R2), product over sum one part opens everything stops only that branch stops one part shorts the rest sees more current that branch draws huge current; fuse opens used for fuses, switches, current sensing outlets, device loads, redundant parts
Series, worked fully
9 V, R1 = 220 ohm, R2 = 470 ohm, in one loop.
R total = 220 + 470 = 690 ohm I = 9 / 690 = 0.013 A, the same everywhere V on R1 = 0.013 x 220 = 2.87 V V on R2 = 0.013 x 470 = 6.13 V check = 2.87 + 6.13 = 9.00 V, the source
The bigger resistance takes the bigger share of the voltage, always, and in exactly the ratio of the resistances: 470 is about 68% of 690, and 6.13 V is about 68% of 9 V. That proportionality is the voltage divider, and boards use it constantly to bring a signal down to a range a chip can read. A divider built from one precise resistor and one drifting one produces a reading wrong by a constant percentage, which is the signature of a calibration problem rather than a failure.
Parallel, worked fully
9 V across R3 = 220 ohm and R4 = 470 ohm.
Each branch sees the full 9 V. I on R3 = 9 / 220 = 0.041 A (41 mA) I on R4 = 9 / 470 = 0.019 A (19 mA) I total = 0.041 + 0.019 = 0.060 A (60 mA) R total = 9 / 0.060 = 150 ohm check = (220 x 470) / 690 = 150 ohm
Two sanity checks live in that block. The total resistance must come out below the smallest branch, because adding a path can only make it easier for current to flow. And the total current must be larger than any single branch. If your answer breaks either rule, you added resistances that should have been combined.
A useful shortcut: equal resistors in parallel divide by how many there are. Two 470 ohm in parallel is 235 ohm; four of them is 117.5 ohm.
Why the building is parallel
Every receptacle in a patient room hangs across the same supply, so each gets the full 120 V and unplugging one device changes nothing for the others. Inside a device the same thinking applies: the display, the controller, the pump motor, and the alarm all hang off the power supply in parallel, each drawing what it needs at the same rail voltage. Series connections in a hospital are reserved for things meant to interrupt everything downstream, which is exactly one list: switches, fuses, breakers, and interlocks.
The old string of holiday lights is the teaching example because the failure is so visible: wired in series, one dead bulb opens the loop and the whole string goes dark, and you have to find the single bad one by testing. Modern strings are wired in parallel sections for exactly that reason.