How to Solve: Resistance Problems

How to Solve: Resistance Problems

Introduction

"If you can solve resistance problems, you can predict why your phone charger gets hot, why Christmas lights all go out when one bulb blows, and—most importantly—you’ll nail those 5-6 mark exam questions that separate a B from an A."

What You Need To Know First

Before diving into resistance problems, you must already understand: 1. Ohm’s Law – The relationship between voltage (V), current (I), and resistance (R): V = I × R. 2. Series vs. Parallel Circuits – How components are connected and how current/voltage behaves in each. 3. Basic Algebra – Rearranging equations to solve for an unknown variable.

If any of these feel shaky, pause here and review them first.

Key Vocabulary

Formulas To Know

Step-by-Step Method

Follow these steps exactly for every resistance problem. No shortcuts.

Step 1: Identify the Circuit Type

• Look at the diagram or description.
• Series? All components in a single path.
• Parallel? Components connected across the same voltage.
• Combination? Both series and parallel parts.

Step 2: Label All Given Values

• Write down every number from the question.
• Example: R₁ = 3 Ω, R₂ = 6 Ω, V = 12 V.

Step 3: Determine What You’re Solving For

• Underline the unknown in the question.
• Example: "Find the current through R₂."

Step 4: Simplify the Circuit

• Replace groups of resistors with their equivalent resistance (R_eq).
• Series: Add resistances.
• Parallel: Use the formula 1/R_eq = 1/R₁ + 1/R₂ + ...
• Redraw the circuit with R_eq if needed.

Step 5: Apply Ohm’s Law

• Use V = I × R to find missing values.
• Rearrange as needed:
• I = V / R
• R = V / I

Step 6: Solve for the Unknown

• Plug in numbers and calculate.
• Check units! (Ω, A, V)

Step 7: Verify Your Answer

• Does it make sense?
• Series: Current should be the same everywhere.
• Parallel: Voltage should be the same across branches.
• If not, recheck your steps.

Worked Example Using the Steps

Question: Two resistors, R₁ = 4 Ω and R₂ = 6 Ω, are connected in series to a 10 V battery. Find the current in the circuit.

Step 1: Identify the circuit type. - Series circuit (single path).

Step 2: Label given values. - R₁ = 4 Ω, R₂ = 6 Ω, V = 10 V

Step 3: Determine what you’re solving for. - Current (I) in the circuit.

Step 4: Simplify the circuit. - Series: R_eq = R₁ + R₂ = 4 Ω + 6 Ω = 10 Ω

Step 5: Apply Ohm’s Law. - V = I × R_eq - Rearrange: I = V / R_eq = 10 V / 10 Ω = 1 A

Step 6: Solve for the unknown. - I = 1 A

Step 7: Verify. - Current in series is the same everywhere. Makes sense.

Answer: The current in the circuit is 1 A.

Worked Examples

Example 1 – Basic (Series Circuit)

Question: Three resistors (R₁ = 2 Ω, R₂ = 3 Ω, R₃ = 5 Ω) are in series with a 12 V battery. Find the total resistance and current.

Solution: 1. Circuit type: Series. 2. Given: R₁ = 2 Ω, R₂ = 3 Ω, R₃ = 5 Ω, V = 12 V 3. Find: R_eq and I. 4. Simplify:
- R_eq = R₁ + R₂ + R₃ = 2 + 3 + 5 = 10 Ω 5. Ohm’s Law:
- I = V / R_eq = 12 V / 10 Ω = 1.2 A 6. Answer:
- Total resistance = 10 Ω
- Current = 1.2 A

What we did and why: - Added resistances because series circuits have a single path. - Used Ohm’s Law to find current because we had voltage and total resistance.

Example 2 – Medium (Parallel Circuit)

Question: Two resistors (R₁ = 6 Ω, R₂ = 3 Ω) are in parallel with a 9 V battery. Find: a) The equivalent resistance. b) The total current from the battery.

Solution: 1. Circuit type: Parallel. 2. Given: R₁ = 6 Ω, R₂ = 3 Ω, V = 9 V 3. Find: R_eq and I_total. 4. Simplify (Parallel):
- 1/R_eq = 1/R₁ + 1/R₂ = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2
- R_eq = 2 Ω 5. Ohm’s Law (Total current):
- I_total = V / R_eq = 9 V / 2 Ω = 4.5 A 6. Answer:
- Equivalent resistance = 2 Ω
- Total current = 4.5 A

What we did and why: - Used the parallel formula because current splits in parallel circuits. - Calculated R_eq first to simplify the circuit before finding current.

Example 3 – Exam Style (Combination Circuit)

Question: A circuit has R₁ = 4 Ω in series with a parallel combination of R₂ = 6 Ω and R₃ = 3 Ω. The battery is 24 V. Find: a) The total resistance. b) The current through R₁.

Solution: 1. Circuit type: Combination (series + parallel). 2. Given: R₁ = 4 Ω, R₂ = 6 Ω, R₃ = 3 Ω, V = 24 V 3. Find: R_eq and I_R1. 4. Simplify (Parallel part first):
- 1/R_parallel = 1/R₂ + 1/R₃ = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2
- R_parallel = 2 Ω 5. Simplify (Series part):
- R_eq = R₁ + R_parallel = 4 Ω + 2 Ω = 6 Ω 6. Ohm’s Law (Total current):
- I_total = V / R_eq = 24 V / 6 Ω = 4 A 7. Current through R₁:
- In series, current is the same everywhere.
- I_R1 = I_total = 4 A 8. Answer:
- Total resistance = 6 Ω
- Current through R₁ = 4 A

What we did and why: - Broke the problem into parts (parallel first, then series). - Used R_eq to find total current, then applied series rules to find I_R1.

Common Mistakes

Exam Traps

1-Minute Recap

"Alright, let’s lock this in. Resistance problems come down to three things: circuit type, simplification, and Ohm’s Law.

1. Series? Add resistances. Current is the same everywhere.
2. Parallel? Use the reciprocal formula. Voltage is the same across branches.
3. Combination? Simplify parallel parts first, then treat the rest as series.

Always: - Label your values. - Find R_eq before touching Ohm’s Law. - Check units and logic—does your answer make sense?

Tonight’s homework: Grab a past paper, find a resistance question, and solve it using these steps. No shortcuts. If you get stuck, go back to the worked examples.

You’ve got this. Now go ace that exam."