Ohm's Law and Basic Circuit Problems: Step-by-Step Practice Set

Overview

The core relationship in introductory circuit analysis is Ohm’s law:

V = IR

where:

• V is voltage in volts (V)
• I is current in amperes (A)
• R is resistance in ohms (Ω)

For many basic circuit problems, this equation is enough to begin. But in practice, you also need a short checklist that tells you what to do first, what values stay the same, and what changes depending on whether the circuit is series, parallel, or mixed.

Use this general method before starting any calculation:

1. Write down what is given. List voltage, current, resistance, or power with units.
2. Sketch or label the circuit. Even a rough diagram helps.
3. Identify the circuit type. Is it a single resistor, series circuit, parallel circuit, or series-parallel combination?
4. Choose the target quantity. Decide whether you are solving for current, voltage drop, equivalent resistance, or power.
5. Apply the correct rule. Use Ohm’s law, series rules, parallel rules, or power formulas.
6. Check units and reasonableness. Larger resistance should usually reduce current for the same source voltage. Voltage drops in series should add to the supply voltage. Branch currents in parallel should add to the total current.

These supporting formulas are used often in worked physics problems about circuits:

• V = IR
• P = VI
• P = I²R
• P = V²/R
• Series resistors: R_total = R₁ + R₂ + ...
• Parallel resistors: 1/R_total = 1/R₁ + 1/R₂ + ...

If rearranging formulas is slowing you down, it helps to review an equation guide such as GCSE Physics Equations List and Rearrangement Guide, A-Level Physics Equations List with Definitions and Unit Checks, or AP Physics Formula Sheet Guide: What Every Equation Means.

Checklist by scenario

This section gives you a scenario-based method you can reuse for common basic circuit problems.

1. Single-resistor Ohm’s law problems

Checklist:

• Identify the two known quantities.
• Choose the Ohm’s law form that isolates the unknown.
• Substitute values with units.
• Round only at the end if needed.

Example: A 12 V battery is connected to a 4 Ω resistor. Find the current.

Given:

• V = 12 V
• R = 4 Ω

Use Ohm’s law:

I = V/R = 12/4 = 3 A

Answer: The current is 3 A.

Quick reason check: A moderate voltage across a small resistance should produce a noticeable current. 3 A is plausible.

2. Solving for resistance from voltage and current

Checklist:

• Make sure current is in amperes, not milliamperes unless converted.
• Rearrange to R = V/I.
• State the answer in ohms.

Example: A component has a voltage of 9 V across it and a current of 0.30 A through it. Find the resistance.

Use:

R = V/I = 9/0.30 = 30 Ω

Answer: The resistance is 30 Ω.

3. Finding voltage drop across a resistor

Checklist:

• Check that current through the resistor is known.
• Use V = IR.
• Make sure the resistor value belongs to the correct part of the circuit.

Example: A current of 2 A flows through a 5 Ω resistor. Find the voltage across it.

V = IR = 2 × 5 = 10 V

Answer: The voltage drop is 10 V.

4. Series circuit problems

In a series circuit, the current is the same everywhere. Resistances add directly.

Checklist:

• Add all resistors to get total resistance.
• Use the supply voltage to find total current.
• Use the same current through each resistor to find individual voltage drops if needed.
• Check that all voltage drops add to the source voltage.

Example: A 12 V supply is connected to two resistors in series: 2 Ω and 4 Ω. Find total resistance, total current, and voltage across each resistor.

Step 1: Total resistance

R_total = 2 + 4 = 6 Ω

Step 2: Total current

I = V/R_total = 12/6 = 2 A

Step 3: Voltage across each resistor

Across 2 Ω:

V₁ = IR = 2 × 2 = 4 V

Across 4 Ω:

V₂ = IR = 2 × 4 = 8 V

Check: 4 V + 8 V = 12 V, which matches the supply.

Answer: Total resistance is 6 Ω, total current is 2 A, and the voltage drops are 4 V and 8 V.

5. Parallel circuit problems

In a parallel circuit, the voltage across each branch is the same. Currents divide between branches.

Checklist:

• Use the same voltage across each branch.
• Find each branch current using I = V/R.
• Add branch currents to find total current.
• If needed, find equivalent resistance using R_total = V/I_total.

Example: A 12 V battery is connected to two resistors in parallel: 6 Ω and 3 Ω. Find branch currents and total current.

Step 1: Voltage across each resistor

Each branch has 12 V across it.

Step 2: Branch currents

I₁ = 12/6 = 2 A

I₂ = 12/3 = 4 A

Step 3: Total current

I_total = 2 + 4 = 6 A

Step 4: Equivalent resistance

R_total = V/I_total = 12/6 = 2 Ω

Answer: The branch currents are 2 A and 4 A, the total current is 6 A, and the equivalent resistance is 2 Ω.

Reason check: The equivalent resistance of parallel resistors should be smaller than the smallest branch resistor. Since 2 Ω is less than 3 Ω, the result is sensible.

6. Series-parallel circuit practice

Mixed circuits are where many students lose track of structure. The safest method is to simplify one step at a time.

Checklist:

• Identify which resistors are definitely in parallel and which are definitely in series.
• Replace one small part of the circuit with its equivalent resistance.
• Redraw the circuit after each simplification.
• Find total current from the supply only after you have the total resistance.
• Work backward to recover branch voltages and currents.

Example: A 12 V source is connected to a 2 Ω resistor in series with two parallel resistors, 3 Ω and 6 Ω. Find total resistance and total current.

Step 1: Combine the parallel part

For 3 Ω and 6 Ω in parallel:

1/R_p = 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2

So, R_p = 2 Ω

Step 2: Add the series resistor

R_total = 2 Ω + 2 Ω = 4 Ω

Step 3: Find total current

I_total = V/R_total = 12/4 = 3 A

Step 4: Find voltage across the series 2 Ω resistor

V = IR = 3 × 2 = 6 V

Step 5: Find voltage across the parallel network

The remaining voltage is 12 V − 6 V = 6 V

Step 6: Find current in each parallel branch

Through 3 Ω branch: I = 6/3 = 2 A

Through 6 Ω branch: I = 6/6 = 1 A

Check: Branch currents add to 3 A, matching the total current.

Answer: Total resistance is 4 Ω and total current is 3 A.

7. Power in circuits

Power questions often appear alongside Ohm’s law. They test whether you can connect energy transfer to voltage, current, and resistance.

Checklist:

• Choose the power formula based on what you know.
• Use P = VI if voltage and current are given.
• Use P = I²R if current and resistance are given.
• Use P = V²/R if voltage and resistance are given.

Example: A 10 Ω resistor carries a current of 2 A. Find the power.

P = I²R = 2² × 10 = 4 × 10 = 40 W

Answer: The resistor dissipates 40 W.

Useful interpretation: Higher current usually increases power quickly because current is squared in P = I²R.

What to double-check

Before finalizing any answer, run through this review list. This is often where marks are saved.

• Units: Are you mixing amperes and milliamperes, or ohms and kilo-ohms? Convert first if needed.
• Circuit type: Did you treat a parallel section like a series section by mistake?
• Same-current rule: In series, current is the same through every component.
• Same-voltage rule: In parallel, voltage is the same across each branch.
• Total resistance: In series, total resistance should increase. In parallel, equivalent resistance should decrease below the smallest branch resistance.
• Voltage sum: In a series loop, voltage drops should add to the supply voltage.
• Current sum: In a parallel circuit, branch currents should add to the total current.
• Significant figures: Match the level expected in your course or lab. For a focused guide, see Significant Figures Rules in Physics: How to Round, Multiply, and Report Results.
• Answer meaning: Ask whether the size of the result makes physical sense.

If your work involves measured values from a practical task, it also helps to review uncertainty and reporting habits in Physics Lab Report Checklist: Sections, Graphs, Uncertainty, and Common Mistakes.

Common mistakes

Most errors in basic circuit problems are not advanced physics errors. They are setup errors. Here are the ones that appear most often.

Confusing series and parallel rules

This is the most common issue. Students may add resistors that are actually in parallel, or use the same current in branches that are not in series. Slow down and identify what the circuit is doing physically. Is there one path for current, or multiple paths?

Using the wrong voltage in a branch

In parallel circuits, each branch has the same potential difference as the supply across that parallel section. In series circuits, the supply voltage is split across components. Many wrong answers come from using the full supply voltage across every resistor in a series circuit.

Solving too early in a mixed circuit

In a series-parallel problem, students often try to find branch currents before simplifying the network. The cleaner method is: reduce the circuit, find total current, then work backward.

Forgetting unit conversions

A current of 250 mA is not 250 A. It is 0.250 A. A resistance of 2 kΩ is 2000 Ω. Missing this can make an answer off by a factor of 1000.

Dropping the final check

A result may be mathematically neat but physically unreasonable. For example, a parallel equivalent resistance larger than every branch resistance should immediately look suspicious.

Power formula mismatch

Using P = V²/R or P = I²R is fine, but only if the voltage or current belongs to the same component. In multi-resistor circuits, be careful not to mix a total current with a single resistor’s voltage unless the relationship is valid for that component.

For students building broader exam revision habits, the checklist style in IB Physics Revision Guide: Topic-by-Topic Formula and Concept Checklist can help structure practice across topics, while Kinematics Problems with Step-by-Step Solutions: Beginner to Advanced shows the same worked-solution mindset in mechanics.

When to revisit

This article is most useful when you treat it as a repeatable pre-problem checklist rather than a one-time read. Revisit it in the following situations:

• Before homework sets on electricity: Use the scenario list to choose the right method quickly.
• Before quizzes and exams: Review the series and parallel rules, then work one example from each type without looking.
• When new circuit types appear: Return once your class adds internal resistance, Kirchhoff’s rules, capacitors, or RC circuits. A good next step is Capacitors and RC Circuits Explained with Charging and Discharging Graphs.
• When lab work begins: Revisit the unit checks, significant figures, and measurement habits before writing up practical results.
• When problem-solving feels slow: Use the checklist to diagnose where you are getting stuck—identifying the circuit type, choosing equations, or checking results.

Action plan:

1. Copy the general method and the review list into your notes.
2. Practice one single-resistor, one series, one parallel, and one mixed problem.
3. After each solution, explain aloud why the current or voltage pattern makes sense.
4. Check every answer using a physical rule, not just algebra.
5. Return to this page whenever your inputs change: new resistor values, new diagram layouts, or new power questions.

That habit is what turns Ohm’s law from a memorized formula into a dependable problem-solving tool. Once that foundation is secure, later topics in electricity and magnetism become much easier to organize and solve.