Electric circuits is the biggest single topic in Grade 12 Physical Science Paper 1. It carries around 55 marks, which means more than a third of Paper 1 depends on whether you understand Ohm's Law, internal resistance, and how current and voltage behave in series and parallel circuits. The reason students lose marks here is not because the physics is difficult. It is because they do not take the time to properly analyse the circuit before they start calculating.
In This Post You Will Learn
✓ The difference between series and parallel circuits and how current and voltage behave in each
✓ How to apply Ohm's Law in combined series-parallel circuits
✓ How internal resistance works and how it affects the terminal voltage of a battery
✓ Step-by-step methods for solving circuit problems in the NSC exam
✓ How to read and interpret circuit diagrams correctly
✓ Where this topic appears in the exam and how to maximise your marks
Series Circuits: How They Work
In a series circuit, all the components are connected one after another in a single loop. There is only one path for the current to follow.
Three rules for series circuits:
Rule 1: The current is the same everywhere.
If the current through the battery is 2 A, then the current through every resistor in that series circuit is also 2 A.
Rule 2: The voltages add up to the total.
The voltage of the battery is shared between the resistors. If V_total = 12 V and there are two resistors, the voltage across each one depends on its resistance.
Rule 3: Resistances add up.
R_total = R1 + R2 + R3 + ...
Example: Three resistors of 2 Ω, 3 Ω, and 5 Ω are connected in series to a 20 V battery (assume no internal resistance).
R_total = 2 + 3 + 5 = 10 Ω
Current: I = V/R = 20/10 = 2 A
Voltage across 2 Ω resistor: V = IR = 2 x 2 = 4 V
Voltage across 3 Ω resistor: V = IR = 2 x 3 = 6 V
Voltage across 5 Ω resistor: V = IR = 2 x 5 = 10 V
Check: 4 + 6 + 10 = 20 V. Correct.
Parallel Circuits: How They Work
In a parallel circuit, the components are connected across each other, creating multiple paths for the current.
Three rules for parallel circuits:
Rule 1: The voltage is the same across each branch.
If the battery provides 12 V, then every parallel branch has 12 V across it.
Rule 2: The currents add up to the total.
The total current from the battery splits between the branches. More current flows through the branch with less resistance.
Rule 3: The total resistance is calculated using the reciprocal formula.
1/R_total = 1/R1 + 1/R2 + 1/R3 + ...
For two resistors in parallel, there is a shortcut:
R_total = (R1 x R2) / (R1 + R2)
Example: Two resistors of 6 Ω and 3 Ω are connected in parallel to a 12 V battery.
R_total = (6 x 3) / (6 + 3) = 18/9 = 2 Ω
Total current: I = V/R = 12/2 = 6 A
Current through 6 Ω: I = V/R = 12/6 = 2 A
Current through 3 Ω: I = V/R = 12/3 = 4 A
Check: 2 + 4 = 6 A. Correct.
Notice that more current flows through the smaller resistor. This is always the case.
Combined Series-Parallel Circuits
Most NSC exam questions involve circuits that have both series and parallel sections. The method is always the same:
Step-by-Step Method for Solving Combined Circuits
Step 1: Identify which resistors are in parallel and which are in series.
Step 2: Calculate the equivalent resistance of the parallel combination first.
Step 3: Add that equivalent resistance to any series resistors to get the total resistance.
Step 4: Use Ohm's Law (V = IR) to find the total current.
Step 5: Work backwards through the circuit to find individual voltages and currents.
Worked Example: Combined Circuit
A circuit has a 24 V battery with no internal resistance. R1 = 4 Ω is in series with a parallel combination of R2 = 6 Ω and R3 = 3 Ω.
Step 1: Find the parallel equivalent of R2 and R3.
R_parallel = (6 x 3) / (6 + 3) = 18/9 = 2 Ω
Step 2: Find the total resistance.
R_total = R1 + R_parallel = 4 + 2 = 6 Ω
Step 3: Find the total current.
I_total = V/R = 24/6 = 4 A
Step 4: Find the voltage across R1.
V_R1 = IR = 4 x 4 = 16 V
Step 5: Find the voltage across the parallel combination.
V_parallel = 24 - 16 = 8 V (or V = IR = 4 x 2 = 8 V)
Step 6: Find the current through each parallel resistor.
I_R2 = V/R = 8/6 = 1.33 A
I_R3 = V/R = 8/3 = 2.67 A
Check: 1.33 + 2.67 = 4 A. Correct.
Internal Resistance and EMF
This is the Grade 12 addition to circuits. In Grade 11, batteries were treated as perfect. In Grade 12, you learn that every battery has internal resistance (r) that causes it to lose some voltage internally.
EMF (ε) is the total energy per unit charge that the battery can provide. It is measured in volts.
Terminal voltage (V_terminal) is the actual voltage available to the external circuit. It is always less than the EMF because some voltage is "lost" inside the battery.
The formula connecting them is:
ε = V_terminal + V_internal
Or equivalently:
ε = I(R + r)
Where R is the total external resistance and r is the internal resistance.
You can also write:
V_terminal = ε - Ir
This tells you that as current increases, the terminal voltage drops. When no current flows (open circuit), V_terminal = ε.
Worked Example: Internal Resistance
A battery has an EMF of 12 V and an internal resistance of 0.5 Ω. It is connected to a 5.5 Ω resistor.
Step 1: Find the total resistance.
R_total = R + r = 5.5 + 0.5 = 6 Ω
Step 2: Find the current.
I = ε / R_total = 12/6 = 2 A
Step 3: Find the terminal voltage.
V_terminal = ε - Ir = 12 - 2(0.5) = 12 - 1 = 11 V
Step 4: Check. The voltage across the external resistor should equal the terminal voltage.
V = IR = 2 x 5.5 = 11 V. Correct.
The "lost volts" inside the battery = Ir = 2 x 0.5 = 1 V. This 1 V is wasted as heat inside the battery.
For full live lessons on this topic, see our Grade 12 Physical Science tuition page.
How to Determine Internal Resistance Experimentally
The NSC exam often asks about the experiment to determine the EMF and internal resistance of a battery. You need to know this.
The experiment involves connecting different external resistors to the battery and measuring the current (I) and terminal voltage (V) each time.
You then plot a graph of V on the y-axis against I on the x-axis.
The result is a straight line with:
y-intercept = ε (the EMF)
gradient = -r (the negative of the internal resistance)
This comes from rearranging V = ε - Ir into y = mx + c form:
V = -rI + ε
So the gradient is -r and the y-intercept is ε.
If you haven't covered the forces section yet, read our guide on Work, Energy and Power Grade 12 - Conservation Explained Simply.
Power in Electric Circuits
Electrical power is the rate at which electrical energy is converted to other forms (heat, light, etc).
There are three formulas for power:
P = VI
P = I²R
P = V²/R
Use whichever formula matches the information you have. If you know V and I, use the first. If you know I and R, use the second. If you know V and R, use the third.
Example: A 4 Ω resistor has 3 A flowing through it.
P = I²R = (3)²(4) = 9 x 4 = 36 W
The resistor converts 36 joules of electrical energy into heat every second.
Common Mistakes Students Make
- Not simplifying the circuit before calculating
Students jump straight into Ohm's Law without first identifying which resistors are in series and which are in parallel. Always redraw the circuit if it is confusing. Simplify parallel combinations into single equivalent resistors, then treat the whole thing as a series circuit.
- Using the wrong voltage in parallel branches
In a parallel section, the voltage is the same across each branch. Students sometimes use the total battery voltage instead of the voltage across the parallel combination. Find the voltage across the parallel section first, then use that to calculate individual branch currents.
- Forgetting to include internal resistance in total resistance
When a question gives you internal resistance, the total resistance is R_external + r, not just R_external. Forgetting r gives you the wrong current, which makes every other calculation wrong too.
- Mixing up EMF and terminal voltage
EMF is the total voltage the battery produces. Terminal voltage is what is available to the external circuit after the internal voltage drop. When a question asks "what is the reading on a voltmeter connected across the battery terminals," they want the terminal voltage (ε - Ir), not the EMF.
- Getting the reciprocal formula wrong for parallel resistors
Students sometimes write R_total = R1 + R2 for parallel resistors, which is the series formula. In parallel, you must use 1/R_total = 1/R1 + 1/R2. After calculating 1/R_total, remember to take the reciprocal to get R_total. Many students forget this last step and write the answer as 1/R instead of R.
How This Topic Appears in the NSC Exam
Electric circuits appears in Paper 1 of the Grade 12 Physical Science NSC exam.
It is the biggest topic in Paper 1, typically carrying between 50 and 55 marks. This alone makes it the most important topic to master.
It usually appears as Question 8 or Question 9 in Paper 1, which means it comes towards the end of the paper. The DBE tends to split it into two or three major sub-questions.
The first part usually gives you a circuit diagram with a combination of series and parallel resistors and a battery with internal resistance. You must calculate the total resistance, the current through the circuit, and the voltage across individual resistors.
The second part often involves changing the circuit in some way. For example, adding or removing a resistor, or opening/closing a switch. You then need to explain what happens to the current, the voltage readings, and the brightness of light bulbs.
The third part may test the experimental determination of EMF and internal resistance. You might be asked to interpret a V vs I graph, identify the EMF from the y-intercept, or calculate the internal resistance from the gradient.
In the 2023 NSC exam, electric circuits appeared as a long multi-part question involving a battery with internal resistance connected to a combination of resistors. Students had to calculate currents, voltages, and power, and then explain what happens when a switch is opened.
The DBE consistently asks qualitative questions like "Will the brightness of bulb X increase, decrease, or remain the same? Explain." These questions test understanding, not calculation. To answer them, think about what happens to the total resistance, then what happens to the total current, then what happens to the voltage and current through each component.
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