What is Voltage?
Voltage (also called potential difference) is the electrical push that drives charge around a circuit. The unit of voltage is the volt (V), named after the Italian physicist Alessandro Volta.
A helpful analogy: think of water flowing through a pipe. Voltage is like the water pressure — the higher the pressure, the harder the water is pushed through. In a circuit, higher voltage pushes electrons more forcefully, which produces a larger current.
A standard AA battery supplies 1.5 V. A phone charger typically supplies 5 V. The mains electricity in Pakistan is 220 V — which is why touching live mains wiring is so dangerous.
- Symbol: V
- Unit: volt (V)
- Measured with: a voltmeter, connected in parallel across a component
What is Current?
Electric current is the rate at which electric charge flows through a conductor. The unit of current is the ampere (A), often shortened to "amp".
Using the water-pipe analogy again: if voltage is the pressure, current is the flow rate — how many litres of water pass a point per second. In circuits, current tells you how many coulombs of charge pass a point per second.
1 ampere = 1 coulomb of charge per second
In practice, many circuits operate with currents smaller than 1 A. Electronics and sensor circuits often use milliamps (mA), where 1 mA = 0.001 A. Always convert milliamps to amps before substituting into Ohm's Law.
- Symbol: I
- Unit: ampere (A)
- Measured with: an ammeter, connected in series in the circuit
What is Resistance?
Resistance is the opposition a material offers to the flow of current. The unit of resistance is the ohm (Ω), named after the German physicist Georg Simon Ohm.
Back to the water analogy: resistance is like the narrowness of the pipe. A thin pipe resists water flow more than a wide pipe. In a circuit, a high-resistance component restricts current — so for the same voltage, a higher resistance produces a lower current.
Every material has a different resistance. Copper wire has very low resistance (which is why we use it in cables). The thin tungsten filament inside a light bulb has high resistance — and that resistance causes it to heat up and glow.
- Symbol: R
- Unit: ohm (Ω)
- Larger values: kilohm (kΩ) = 1 000 Ω, megohm (MΩ) = 1 000 000 Ω
Ohm's Law: V = I × R
Georg Simon Ohm published his law in 1827. After careful experiments with metal wires, he discovered a consistent relationship: for a conductor at constant temperature, the voltage across it is directly proportional to the current through it.
In equation form:
Where:
- V = voltage in volts (V)
- I = current in amperes (A)
- R = resistance in ohms (Ω)
The law means: doubling the voltage doubles the current (if resistance stays constant). Doubling the resistance halves the current (if voltage stays constant). This proportional relationship is the core of circuit analysis at O Level.
The Ohm's Law Triangle
Many students use the "VIR triangle" to remember the rearrangements. Write V at the top, I on the bottom-left, and R on the bottom-right. Cover the quantity you want to find, and the remaining two show the operation:
- Cover V → you see I × R → so V = I × R
- Cover I → you see V ÷ R → so I = V ÷ R
- Cover R → you see V ÷ I → so R = V ÷ I
8 Worked Examples
Work through each example carefully. Notice how every solution follows the same four-step method: identify → select formula → substitute → calculate and state units.
Example 1 — Find Voltage
Question: A resistor carries a current of 3 A and has a resistance of 8 Ω. Calculate the voltage across it.
Given: I = 3 A, R = 8 Ω
Find: V
Formula: V = I × R
Substitute: V = 3 × 8
Answer: V = 24 V
Example 2 — Find Current
Question: A 12 V battery connects to a 4 Ω resistor. What current flows through the circuit?
Given: V = 12 V, R = 4 Ω
Find: I
Formula: I = V ÷ R
Substitute: I = 12 ÷ 4
Answer: I = 3 A
Example 3 — Find Resistance
Question: A 9 V battery drives a current of 0.5 A through a resistor. What is the resistance?
Given: V = 9 V, I = 0.5 A
Find: R
Formula: R = V ÷ I
Substitute: R = 9 ÷ 0.5
Answer: R = 18 Ω
Example 4 — Converting Milliamps
Question: A circuit has a resistance of 500 Ω and a current of 40 mA flows through it. Find the voltage.
Convert first: 40 mA = 40 ÷ 1000 = 0.04 A
Given: I = 0.04 A, R = 500 Ω
Find: V
Formula: V = I × R
Substitute: V = 0.04 × 500
Answer: V = 20 V
Key lesson: always convert mA to A before using the formula.
Example 5 — Series Circuit
Question: Two resistors of 6 Ω and 4 Ω are connected in series. A 20 V battery is connected across them. Find the current in the circuit.
Step 1 — Find total resistance:
Rtotal = 6 + 4 = 10 Ω
Step 2 — Apply Ohm's Law:
I = V ÷ R = 20 ÷ 10
Answer: I = 2 A
Example 6 — Finding Resistance from a Graph
Question: A V–I graph for a resistor shows that when V = 6 V, I = 0.3 A. Calculate the resistance.
Formula: R = V ÷ I
Substitute: R = 6 ÷ 0.3
Answer: R = 20 Ω
On a V–I graph, resistance equals the gradient (slope) of the line. A steeper line means higher resistance.
Example 7 — Two Step Problem
Question: Three resistors of 10 Ω, 15 Ω, and 25 Ω are connected in series to a 100 V supply. Find (a) the total resistance and (b) the current in the circuit.
(a) Total resistance:
Rtotal = 10 + 15 + 25 = 50 Ω
(b) Current:
I = V ÷ R = 100 ÷ 50
Answer: I = 2 A
Example 8 — Find Voltage Across One Resistor
Question: Using the circuit from Example 7 (I = 2 A), find the voltage across the 15 Ω resistor.
Formula: V = I × R
Substitute: V = 2 × 15
Answer: V = 30 V
Notice: in a series circuit the voltages across individual resistors add up to the total supply voltage (30 + 20 + 50 = 100 V ✓).
Resistance in Series Circuits
When you connect resistors in series, you place them one after another so that the same current flows through each one. To find the total resistance, simply add all individual resistances together.
Key facts about series circuits:
- The current is the same at every point in the circuit.
- The voltages across each component add up to the supply voltage (Vtotal = V1 + V2 + …).
- Adding more resistors in series increases total resistance and decreases current.
Resistance in Parallel Circuits
When you connect resistors in parallel, you give current multiple paths to travel. The total resistance of a parallel combination is less than the smallest individual resistor.
Key facts about parallel circuits:
- The voltage is the same across every branch.
- The currents in each branch add up to the total current from the source.
- Adding more resistors in parallel decreases total resistance and increases total current drawn.
This is why household appliances connect in parallel. Each appliance receives the full mains voltage (220 V), and switching one off does not affect the others.
Common Mistakes Students Make
After reviewing hundreds of student solutions, these are the errors that cost marks most often:
- Forgetting to convert milliamps. If the question gives current in mA, divide by 1 000 to get amps before substituting. Writing "I = 40 mA" into the formula gives a wrong answer every time.
- Using the wrong formula. Students sometimes write V = I ÷ R by mistake. Remember: V and I are on the same "level" in the triangle — one multiplied by the other. Resistance always divides.
- Omitting units in the answer. Writing "V = 24" scores no marks. Always write the unit: "V = 24 V".
- Adding resistors in parallel using the series formula. In a parallel circuit, you cannot add resistors directly. Use the reciprocal formula.
- Not showing working. Even if your final answer is wrong, correct working earns method marks in O Level papers.
O Level Exam Tips
- Read the question twice. Identify every value given (V, I, R) and what you are asked to find before writing anything.
- Write the formula first. Always start your working with the correct version of Ohm's Law, then substitute values. Examiners reward structured answers.
- Check your units. Volts, amperes, and ohms must be consistent. Never mix mA and A in the same calculation.
- In series circuits, find total resistance first. Sum all resistors before applying V = IR.
- Check with a sense test. More resistance → less current. If your answer contradicts this, recheck your substitution.
- For V–I graph questions, remember that the slope (gradient) of the line equals resistance. A straight line through the origin confirms Ohm's Law holds.
Practice Questions
Try these yourself before checking the answers below.
- A 6 V battery connects to a 30 Ω resistor. Find the current.
- A current of 2 A flows through a 12 Ω resistor. Find the voltage.
- A 9 V source drives 180 mA through a resistor. Find the resistance.
- Three 20 Ω resistors connect in series to a 60 V supply. Find the current.
- A voltmeter reads 15 V and an ammeter reads 0.5 A. What is the resistance?
Show Answers
- I = 6 ÷ 30 = 0.2 A
- V = 2 × 12 = 24 V
- Convert 180 mA → 0.18 A. R = 9 ÷ 0.18 = 50 Ω
- Rtotal = 60 Ω. I = 60 ÷ 60 = 1 A
- R = 15 ÷ 0.5 = 30 Ω