Series Circuit Formula

Series circuit is a circuit arrangement in which components are connected end-to-end along a single path, so exactly the same current flows through every.

The Formula

Rtotal=R1+R2+R3+…R_{\text{total}} = R_1 + R_2 + R_3 + \ldots (resistances add up)

When to use: Like cars on a single-lane road — every car (charge) must pass through every toll booth (component) in order.

Quick Example

Old-style Christmas lights in series: one burns out and they all go dark because the circuit is broken.

Notation

ReqR_{\text{eq}} is the total (equivalent) resistance in ohms (Ω\Omega), RiR_i is the resistance of the ii-th component, II is the common current in amperes, and Vi=IRiV_i = IR_i is the voltage drop across each component.

What This Formula Means

A circuit arrangement in which components are connected end-to-end along a single path, so exactly the same current flows through every component.

Like cars on a single-lane road — every car (charge) must pass through every toll booth (component) in order.

Formal View

For nn resistors in series carrying common current II, the equivalent resistance is Req=∑i=1nRiR_{\text{eq}} = \sum_{i=1}^{n} R_i. By Kirchhoff's voltage law, Vsource=∑i=1nVi=I∑i=1nRiV_{\text{source}} = \sum_{i=1}^{n} V_i = I \sum_{i=1}^{n} R_i.

Worked Examples

Example 1

medium
Three resistors (4 Ω4 \text{ } \Omega, 6 Ω6 \text{ } \Omega, 10 Ω10 \text{ } \Omega) are connected in series to a 20 V20 \text{ V} battery. What is the current and the voltage across each resistor?

Answer

I=1 A;V1=4 V,V2=6 V,V3=10 VI = 1 \text{ A}; \quad V_1 = 4 \text{ V}, V_2 = 6 \text{ V}, V_3 = 10 \text{ V}

First step

1
Total resistance: RT=4+6+10=20 ΩR_T = 4 + 6 + 10 = 20 \text{ } \Omega.

See the full worked solution + why-it-works coaching

SetupKey insightWhy it worksCommon pitfallConnection

Unlock answer keys One Family plan — every worked solution, all subjects

Example 2

hard
A 6 V6 \text{ V} battery powers a series circuit with a 3 Ω3 \text{ } \Omega resistor and an unknown resistor. The current is 0.5 A0.5 \text{ A}. Find the unknown resistance and the power dissipated by each resistor.

Example 3

medium
A 24 V24 \text{ V} battery drives resistors R1=2 ΩR_1 = 2 \text{ } \Omega, R2=4 ΩR_2 = 4 \text{ } \Omega, R3=6 ΩR_3 = 6 \text{ } \Omega in series. Find (a) the current and (b) the voltage across R3R_3.

Common Mistakes

  • Thinking the current decreases as it passes through each resistor — the current is identical at every point in a series circuit; it is the voltage that drops across each component. - Fix this by naming the system, checking "Can I identify the circuit path, what quantity is flowing or changing, and which electrical rule links the quantities?", and attaching units or direction to the final statement.
  • Using the parallel resistance formula (1/R1/R) for series components — in series, resistances simply add: Rtotal=R1+R2+…R_{\text{total}} = R_1 + R_2 + \ldots - Fix this by naming the system, checking "Can I identify the circuit path, what quantity is flowing or changing, and which electrical rule links the quantities?", and attaching units or direction to the final statement.
  • Forgetting that if one component breaks (open circuit), the entire series circuit stops — there is only one current path, so a break anywhere halts all current flow. - Fix this by naming the system, checking "Can I identify the circuit path, what quantity is flowing or changing, and which electrical rule links the quantities?", and attaching units or direction to the final statement.
  • Using series circuit from a keyword alone - Signal words like charge, current, voltage only point to a possible model; the system must match too.

Why This Formula Matters

Series Circuit helps students reason about circuits as systems rather than as disconnected parts. It makes household devices, sensors, motors, and electronics easier to interpret because every electrical effect depends on paths and potential differences.

Frequently Asked Questions

What is the Series Circuit formula?

A circuit arrangement in which components are connected end-to-end along a single path, so exactly the same current flows through every component.

How do you use the Series Circuit formula?

Like cars on a single-lane road — every car (charge) must pass through every toll booth (component) in order.

What do the symbols mean in the Series Circuit formula?

ReqR_{\text{eq}} is the total (equivalent) resistance in ohms (Ω\Omega), RiR_i is the resistance of the ii-th component, II is the common current in amperes, and Vi=IRiV_i = IR_i is the voltage drop across each component.

Why is the Series Circuit formula important in Physics?

Series Circuit helps students reason about circuits as systems rather than as disconnected parts. It makes household devices, sensors, motors, and electronics easier to interpret because every electrical effect depends on paths and potential differences.

What do students get wrong about Series Circuit?

Students often know a formula related to series circuit but skip the recognition step: Can I identify the circuit path, what quantity is flowing or changing, and which electrical rule links the quantities? That leads to a correct-looking substitution attached to the wrong physical model.

What should I learn before the Series Circuit formula?

Before studying the Series Circuit formula, you should understand: circuit, resistance, ohms law.

← Back to Series Circuit See All Examples Practice Problems