Exercises: Series Circuits

Work through each section in order. Show all steps: find R_eq, then I, then each voltage drop, then verify with KVL.

Grade 11·21 problems·~30 min·OpenStax Physics (High School)·section·sec-19-2

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Recall / Warm-Up

Which of the following is the defining property of a series circuit?

There is only one path for current to flow, so all components share the same current.

Each component has the same voltage across it.

The total resistance equals the smallest individual resistance.

Each component can be switched on or off independently.

In a series string of five holiday lights, one bulb burns out (its filament breaks, creating an open circuit). What happens to the other four bulbs?

All four go out — the open circuit breaks the single current path.

The other four get brighter — less resistance means more current.

The other four stay on — the current finds a path around the broken bulb.

Only the bulbs after the broken one go out.

Kirchhoff's Voltage Law (KVL) states that in any closed loop of a circuit:

The sum of all voltage drops across components equals the source voltage.

The current entering a junction equals the current leaving a junction.

KVL only applies to simple series circuits with one loop.

The voltage drops across all resistors are equal.

Fluency Practice

Three resistors — $R_1 = 10\ \Omega$ , $R_2 = 15\ \Omega$ , and $R_3 = 25\ \Omega$ — are connected in series. What is the equivalent resistance?

Two resistors in series have a combined equivalent resistance of $R_{eq} = 45\ \Omega$ . One resistor has $R_1 = 18\ \Omega$ . What is the resistance of the other resistor?

Series circuit diagram with a 12 V battery and three resistors (10 Ω, 20 Ω, 30 Ω) connected in a single loop with current I flowing through all.

A series circuit contains three resistors ( $R_1 = 10\ \Omega$ , $R_2 = 20\ \Omega$ , $R_3 = 30\ \Omega$ ) connected to a $V_{source} = 12\ \text{V}$ battery. What current flows through the circuit?

Using the same circuit from fluency-3 ( $R_1 = 10\ \Omega$ , $R_2 = 20\ \Omega$ , $R_3 = 30\ \Omega$ , $V_{source} = 12\ \text{V}$ , $I = 0.20\ \text{A}$ ), what is the voltage drop across $R_3$ ?

In the same series circuit ( $R_1 = 10\ \Omega$ , $R_2 = 20\ \Omega$ , $R_3 = 30\ \Omega$ , $I = 0.20\ \text{A}$ ), what is the KVL check result: do the voltage drops across all three resistors sum to $V_{source} = 12\ \text{V}$ ?

Yes: $V_1 + V_2 + V_3 = 2 + 4 + 6 = 12\ \text{V}$ ✓

No: the drops sum to $6\ \text{V}$ , only half the source.

No: the drops cannot be calculated from the current and resistances.

Yes, but only because this is a simple circuit — KVL doesn't apply in general.

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