Series Circuit Formula

The Formula

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.

What This Formula Means

A circuit in which components are connected end-to-end, so the same current flows through each one.

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

Worked Examples

Example 1

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

Solution

  1. 1
    Total resistance: R_T = 4 + 6 + 10 = 20 \text{ } \Omega.
  2. 2
    Current (same through all): I = \frac{V}{R_T} = \frac{20}{20} = 1 \text{ A}
  3. 3
    Voltage drops: V_1 = IR_1 = 4 \text{ V}, V_2 = IR_2 = 6 \text{ V}, V_3 = IR_3 = 10 \text{ V}.
  4. 4
    Check: 4 + 6 + 10 = 20 \text{ V} (matches battery voltage).

Answer

I = 1 \text{ A}; \quad V_1 = 4 \text{ V}, V_2 = 6 \text{ V}, V_3 = 10 \text{ V}
In a series circuit, current is the same through all components. Resistances add directly, and the battery voltage divides among the resistors proportionally to their resistances.

Example 2

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

Why This Formula Matters

Series circuits are simple to analyze and appear in voltage dividers and sensor circuits.

Frequently Asked Questions

What is the Series Circuit formula?

A circuit in which components are connected end-to-end, so the same current flows through each one.

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.

Why is the Series Circuit formula important in Physics?

Series circuits are simple to analyze and appear in voltage dividers and sensor circuits.

What do students get wrong about Series Circuit?

Adding more resistors in series increases total resistance and decreases current.

What should I learn before the Series Circuit formula?

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

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