By H.L.M. Lee – Updated March 24, 2022

In a series circuit, components are arranged one after another, forming a single closed path for current. The battery powers the loop, forcing the same current to flow through each resistor. Think of the battery as a water pump, current as water, and resistors as houses in a row: the water must pass through each house sequentially before returning to the pump.

Ohm’s law links voltage, current, and resistance:

\(V = IR\)

where V is the voltage across a resistor, I is the current through it, and R is the resistance. In series, because the current is identical for every element, the voltage drop across each resistor depends solely on its resistance.

What Is a Parallel Connection?

A parallel circuit connects components like the rungs of a ladder. Each device sits on its own branch of the supply, so the same voltage appears across every resistor, but each can draw a different amount of current based on its resistance. Ohm’s law for current is expressed as I = V/R.

Calculating Equivalent Resistance

For a series arrangement of resistors R₁, R₂, R₃, …, the equivalent resistance is the simple sum:

\(R_s = R_1 + R_2 + R_3 + …\)

Adding a resistor to a series circuit always raises the overall resistance.

In contrast, resistors in parallel act as a single resistor whose equivalent resistance is found using:

\(\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + …\)

Adding a resistor in parallel always reduces the total resistance, a fact that underpins many practical advantages and disadvantages of this topology.

Advantages of Parallel Wiring

• Devices operate independently: plugging a refrigerator into a kitchen outlet does not alter the voltage or current available to other appliances.
• Redundancy: in a string of modern Christmas lights, if one bulb fails, the remaining bulbs stay lit, making troubleshooting straightforward.
• Predictable voltage: every component sees the same supply voltage, simplifying design and safety calculations.

Disadvantages of Parallel Wiring

• Short‑circuit risk: a low‑resistance fault (e.g., a jammed wire across an outlet) forces excessive current through the circuit, potentially causing sparks, overheating, and fire.
• Higher overall current draw: because resistance is lowered, more current flows for a given voltage, which can lead to higher power consumption and the need for robust fusing or circuit protection.

Fortunately, protective devices such as fuses are placed in series with the wiring. In the event of a short circuit, the fuse blows, breaking the circuit and preventing damage.