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Electric circuits

Paper 1Paper 2Paper 3Paper 4Paper 5Paper 6

This topic is examined in Paper 1, Paper 2, Paper 3, Paper 4, Paper 5, and Paper 6.

Circuit Components and Symbols
To draw and interpret circuit diagrams, you must know the standard symbols for components. These are the 'vocabulary' of electricity.
Function / Behavior
Provides the electromotive force (e.m.f.) or voltage to drive current.
Converts mechanical energy into electrical energy (e.g., in power stations).
Opens (breaks) or closes (completes) the circuit.
Opposes current flow. Resistance is constant.
Allows resistance to be changed, thereby controlling current or p.d.
Converts electrical energy into thermal energy.
Resistance decreases as temperature increases.
Resistance decreases as light intensity increases.
Converts electrical energy into light and heat. Resistance changes with temperature.
Converts electrical energy into kinetic (mechanical) energy.
Produces sound when current flows.
Measures current. Must be connected in series.
Measures potential difference (p.d.). Must be connected in parallel.
Allows current to flow in only one direction (forward bias). Blocks current in reverse.
Emits light when forward biased. Must be used with a series resistor to prevent burning out.
Creates a magnetic field when current flows.
Changes the voltage of an alternating current (a.c.) supply.
Melts and breaks the circuit if current exceeds a safe limit.
An electromechanical switch. A small current in the coil creates a magnetic field that closes a separate high-current circuit.
Series vs. Parallel Circuits
Series Circuit: Components are connected in a single loop. There is only one path for the current to flow.

Parallel Circuit: Components are connected in multiple branches (loops). The current splits at junctions and recombines.

Current in Series (Learning Objective 3):
The current is the same at every point in a series circuit. Charge cannot accumulate or disappear, so the rate of flow (current) must be constant throughout the single loop.

Current in Parallel (Learning Objective 7 & 10a):

  1. The total current from the source is larger than the current in any single branch because it splits among the paths.
  2. Kirchhoff’s First Law: The sum of currents entering a junction equals the sum of currents leaving it (I_{in} = I_{out}). This is due to the conservation of charge.

Potential Difference (p.d.) Rules (Learning Objective 10b & 10c):

  1. Series: The total p.d. across the source equals the sum of the individual p.d.s across each component (V_{total} = V_1 + V_2 + ...). Energy supplied per coulomb is shared among components.
  2. Parallel: The p.d. across any branch in a parallel arrangement is the same as the p.d. across the source (and any other parallel branch). V_{branch} = V_{source}.
Resistance Calculations
Resistors in Series (Learning Objective 6):
When resistors are in series, their resistances add up. The total resistance is greater than any individual resistor.

R_{total} = R_1 + R_2 + R_3 + ...

where R is resistance in ohms (\Omega).

Resistors in Parallel (Learning Objective 8 & 12):
When resistors are in parallel, the combined resistance is less than the smallest individual resistor. This is because connecting paths side-by-side increases the total cross-sectional area available for current flow.

For two resistors:
\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2}

Or, using the product-over-sum formula (often easier for calculation):
R_{total} = \frac{R_1 \times R_2}{R_1 + R_2}

Combined e.m.f. of Cells in Series (Learning Objective 5):
When cells are connected in series (positive to negative), their voltages add up.

V_{total} = V_1 + V_2 + ...

Ohm's Law and Resistance Behavior

Learning Objective 13: Relationship between p.d., Current, and Resistance.
For a constant current I, the potential difference V across an electrical conductor is directly proportional to its resistance R.

V = I \times R

Therefore:

  • If the current I is kept constant and the resistance R increases, the p.d. V increases.
  • This is because a higher resistance requires more energy (work) to push the same amount of charge through it, resulting in a larger voltage drop.
Variable Potential Divider (Learning Objective 14 & 15):
A potential divider uses two resistors in series to split the source voltage. It allows you to obtain a variable p.d. from 0V up to the source voltage.

The Principle: The p.d. is shared between the resistors in proportion to their resistance values.

\frac{R_1}{R_2} = \frac{V_1}{V_2}

where:

  • R_1, R_2 are the resistances of the two components.
  • V_1, V_2 are the potential differences across them.

Application: If you use a variable resistor (potentiometer) as one part of the divider, moving the wiper changes R_1 and R_2, thus changing V_1 and V_2. This is distinct from a simple series variable resistor which only controls current; a potential divider specifically provides a variable voltage output.

Calculating Parallel Resistance
Question: Calculate the combined resistance of a 60,\Omega resistor and a 30,\Omega resistor connected in parallel.

Step 1: Choose the formula.
Using the product-over-sum method for two resistors:
R_{total} = \frac{R_1 \times R_2}{R_1 + R_2}

Step 2: Substitute values.
R_{total} = \frac{60 \times 30}{60 + 30}

Step 3: Calculate.
R_{total} = \frac{1800}{90} = 20,\Omega

Check: The result (20,\Omega) is less than the smallest resistor (30,\Omega), which confirms the rule for parallel circuits.

⚠︎ Thermistor and LDR Behavior

Mistake: Thinking that heating a thermistor increases its resistance, or that darkness increases an LDR's resistance in a way that increases current.

Correct Understanding:

  • Thermistor (NTC): As temperature increases, resistance decreases. Therefore, in a series circuit with a fixed resistor, the current increases and the p.d. across the thermistor decreases (while p.d. across the fixed resistor increases).
  • LDR: As light intensity decreases (gets darker), resistance increases. Therefore, in a series circuit, the current decreases.
Mistake: Adding parallel resistances directly (e.g., 60 + 30 = 90,\Omega).

Correct Understanding: Parallel resistance is always less than the smallest individual resistor. Always use the reciprocal formula or product-over-sum.

Explaining Advantages of Parallel Lighting Circuits
When to use: When asked why household or lighting circuits are wired in parallel.

Why examiners accept this: Examiners look for two key physical advantages: independence of components and constant voltage.

Correct Phrasing:

  1. "If one lamp breaks (filament fails), the other lamps remain lit because they are on separate branches." (Independence)
  2. "Each lamp receives the full source voltage (e.g., 230 V or 12 V), so they shine at full brightness." (Constant p.d.)

Example: 'The advantage of connecting lamps in parallel is that if one lamp blows, the others continue to work, and each lamp operates at the full supply voltage.'

When to use: When asked why a variable resistor is preferred over changing cells or resistors manually.

Why examiners accept this: Examiners value the ability to obtain continuous and precise values without breaking the circuit.

Correct Phrasing:
"A variable resistor allows you to obtain a continuous range of current/resistance values easily and quickly, without having to disconnect the circuit or swap components."

Example: 'The advantage of using a variable resistor is that it allows for easy adjustment of the current to specific desired values.'

Past Paper Style Questions
Q:
State two advantages of connecting lamps in parallel in a lighting circuit.
A:
  1. If one lamp breaks, the others remain lit. 2. Each lamp gets the full supply voltage (so they are all equally bright).
Q:
A student heats a thermistor in a series circuit with a fixed resistor and a battery. Describe what happens to the current in the circuit.
A:
The resistance of the thermistor decreases as it gets hotter. Therefore, the total resistance of the circuit decreases, causing the current to increase.
Q:
Calculate the combined resistance of two resistors, R_1 = 10,\Omega and R_2 = 15,\Omega, connected in parallel.
A:
Using R_{total} = \frac{R_1 R_2}{R_1 + R_2}:
R_{total} = \frac{10 \times 15}{10 + 15} = \frac{150}{25} = 6,\Omega.
Q:
Explain why the p.d. across a conductor increases if its resistance increases while the current remains constant.
A:
According to V = IR, if I is constant, V is directly proportional to R. A higher resistance requires more energy per coulomb of charge to pass through, resulting in a larger potential difference.
Q:
In a potential divider circuit with resistors R_1 and R_2, if R_1 = 20,\Omega and R_2 = 40,\Omega, what is the ratio of the p.d. across R_1 to the p.d. across R_2?
A:
The p.d. is shared in proportion to resistance. Ratio V_1 : V_2 = R_1 : R_2 = 20 : 40 = 1 : 2.
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