Resistance Revision Notes

Electrical resistance is a measure of how much a component or material opposes the flow of electric current through it.

It is defined as the ratio of the potential difference (voltage) across the component to the current flowing through it.

Mathematically, resistance R is given by R = V / I, where V is the potential difference in volts (V) and I is the current in amperes (A).

• Resistance is a scalar quantity measured in ohms (Ω).
• 1 ohm (Ω) is the resistance when a potential difference of 1 volt causes a current of 1 ampere to flow.

Ohm's law states that, for many conductors at constant temperature, the current flowing through the conductor is directly proportional to the potential difference across it.

This relationship can be expressed as V = IR, where V is potential difference, I is current, and R is resistance.

From this, resistance can be calculated by rearranging the formula to R = V / I.

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

To calculate resistance, measure the potential difference across the component and the current through it, then use R = V / I.

To find potential difference, rearrange to V = IR.

To find current, rearrange to I = V / R (though this is beyond the current objective).

• Always include units in calculations to ensure correctness.
• Example: If V = 12 V and I = 3 A, then R = 12 V / 3 A = 4 Ω.
• Common error: forgetting to convert units or mixing units leads to incorrect answers.

Resistance arises because electrons moving through a conductor collide with atoms, losing energy and slowing down the flow of charge.

Higher resistance means less current for a given potential difference.

Resistance depends on material, length, cross-sectional area, and temperature (covered in other objectives).

• A resistor is a component designed to have a specific resistance.
• Ohmic conductors obey Ohm's law; their resistance remains constant over a range of voltages and currents.

To measure the resistance of a resistor, you need the following apparatus: a resistor (or component whose resistance is to be measured), a power supply (such as a battery or DC power supply), an ammeter, a voltmeter, connecting wires, and a switch.

Connect the circuit as follows: connect the ammeter in series with the resistor and the power supply. This arrangement allows the ammeter to measure the current flowing through the resistor.

Connect the voltmeter in parallel across the resistor. This means the voltmeter's two terminals connect to the two ends of the resistor, enabling it to measure the potential difference (voltage) across it.

• Ammeter connected in series with the resistor to measure current (I).
• Voltmeter connected in parallel across the resistor to measure voltage (V).
• Power supply provides the driving voltage for current flow.
• Switch included to control the circuit safely.

1. Assemble the circuit as described, ensuring all connections are secure.

2. Close the switch to allow current to flow through the circuit.

3. Record the current reading from the ammeter (in amperes, A). Note that the ammeter should have a low resistance to avoid affecting the circuit current significantly, but this is usually negligible for school experiments.

• 4. Record the voltage reading from the voltmeter (in volts, V).
• 5. Repeat the readings several times, possibly varying the voltage by adjusting the power supply if possible, to obtain multiple pairs of current and voltage values.
• 6. Open the switch and disconnect the circuit after measurements are complete.

Ohm's Law states that the resistance R of a component is the ratio of the voltage V across it to the current I flowing through it:

R = V / I, where R is resistance in ohms (Ω), V is voltage in volts (V), and I is current in amperes (A).

To calculate resistance: substitute the measured voltage and current values into the formula. For example, if V = 6.0 V and I = 0.20 A, then: R = 6.0 V / 0.20 A = 30 Ω.

• Always include units in calculations to ensure correctness.
• If multiple readings are taken, calculate resistance for each pair and find an average to improve accuracy.
• Be aware that some components do not have constant resistance; this method assumes the resistor behaves ohmically (constant resistance).

To improve the reliability of the resistance measurement:

Take multiple readings of voltage and current and calculate an average resistance.

Ensure connections are tight to reduce contact resistance errors, which can affect readings especially at low resistance values.

• Use a suitable range on the ammeter and voltmeter to get precise readings without overloading the instruments.
• Keep the temperature of the resistor constant, as resistance can change with temperature.
• Use a variable power supply to vary voltage and check if resistance remains constant, confirming ohmic behaviour.
• Record uncertainties in measurements and consider them when reporting results.

Use low voltages to prevent overheating the resistor or damaging the meters.

Do not exceed the current rating of the resistor or ammeter to avoid damage or hazards.

Switch off the power supply before changing the circuit connections to prevent electric shock or short circuits.

• Handle equipment carefully to avoid damage.
• Ensure the voltmeter has a high resistance to prevent it from drawing significant current and affecting the circuit.
• Check the polarity of meters before connecting to avoid incorrect readings or damage.

Resistance is a measure of how much a material opposes the flow of electric current. It is a scalar quantity measured in ohms (Ω). A higher resistance means less current flows for a given potential difference across the material.

In metallic wires, resistance arises because free electrons collide with fixed metal ions as they move through the wire, losing energy and slowing down the current flow.

• Resistance (R) is measured in ohms (Ω).
• It quantifies opposition to current flow.
• Caused by collisions between electrons and metal ions.

The resistance of a metallic wire is directly proportional to its length. This means that if the length of the wire doubles, its resistance also doubles.

Physically, a longer wire contains more metal ions, so electrons collide more frequently, increasing resistance.

For example, a 2 m wire has twice the resistance of a 1 m wire made of the same material and thickness.

• Resistance ∝ Length (R ∝ L).
• Longer wire → more collisions → higher resistance.
• Doubling length doubles resistance.

Resistance is inversely proportional to the cross-sectional area of the wire. A wire with a larger cross-sectional area has lower resistance.

This is because a thicker wire provides more paths for electrons to flow, reducing the chance of collisions and allowing more current to pass.

For example, doubling the cross-sectional area halves the resistance, assuming length and material remain constant.

• Resistance ∝ 1 / Cross-sectional area (R ∝ 1/A).
• Thicker wire → more electron paths → lower resistance.
• Doubling area halves resistance.

Combining these relationships, resistance depends on both length and cross-sectional area as:

R ∝ L / A, where R is resistance, L is length, and A is cross-sectional area.

This means resistance increases with length and decreases with cross-sectional area for a wire of uniform material and temperature.

• Resistance increases with length.
• Resistance decreases with cross-sectional area.
• R ∝ L / A (qualitative relationship).

Electrons moving through a wire collide with metal ions, losing energy and causing resistance.

Longer wires have more ions to collide with, increasing resistance.

Thicker wires have more space for electrons to flow, reducing collisions and resistance, similar to how a wider pipe allows more water flow with less friction loss.

• Resistance caused by electron-ion collisions.
• Longer wire → more collisions → higher resistance.
• Thicker wire → more flow paths → lower resistance.
• Important for designing circuits to minimise energy loss.

The current-voltage (I-V) characteristic of an electrical component is a graph showing how the current (I, in amperes, A) flowing through the component varies with the potential difference (voltage, V, in volts, V) across it.

The shape of the I-V graph reveals important information about the component's electrical behaviour and resistance.

The voltage is plotted on the horizontal (x) axis and the current on the vertical (y) axis.

• Voltage (V) on x-axis, Current (I) on y-axis.
• Gradient of I-V graph = 1 / resistance (R) for ohmic components.
• Non-linear graphs indicate changing resistance.

A resistor with constant resistance obeys Ohm's Law, which states that the current through the resistor is directly proportional to the voltage across it, provided the temperature remains constant.

Mathematically, this is expressed as V = IR, where R is the resistance in ohms (Ω).

The I-V graph for such a resistor is a straight line passing through the origin, indicating a constant resistance.

• Ohm's Law: V = IR
• Graph is a straight line through origin.
• Gradient = 1/R (steeper line means lower resistance).

A filament lamp does not have a constant resistance because its filament heats up as current flows through it.

As the filament temperature increases, its resistance increases due to increased atomic vibrations that impede electron flow.

The I-V graph is a curve that starts steep (low resistance at low temperature) and gradually flattens as voltage and current increase, showing a non-linear relationship.

• Resistance increases with temperature.
• Graph is a curve, not a straight line.
• At low voltage, resistance is low; at high voltage, resistance is higher.

A diode allows current to flow primarily in one direction and blocks it in the opposite direction.

In the forward direction, the diode shows very little current until a threshold voltage (about 0.6–0.7 V for silicon diodes) is reached.

After this threshold, current increases rapidly with voltage, producing a steep curve on the I-V graph in the forward direction, while in the reverse direction, current is almost zero (except for a tiny leakage current).

• Current flows only after threshold voltage (~0.6 V for silicon).
• Graph shows almost zero current below threshold.
• Current in reverse direction is negligible.

To sketch the I-V graph for each component, label the axes with voltage (V) on the x-axis and current (A) on the y-axis.

For the resistor, draw a straight line through the origin with constant gradient.

For the filament lamp, draw a curve starting steep near the origin and flattening as voltage increases, showing increasing resistance with temperature rise due to heating of the filament wire (usually tungsten). The resistance increases because the filament's atoms vibrate more at higher temperatures, scattering electrons more and reducing current increase rate relative to voltage increase (non-ohmic behaviour). For the diode, draw a graph with almost zero current along the x-axis in the negative voltage region (reverse bias), and in the positive voltage region (forward bias), a flat line near zero current until the threshold voltage, then a sharp rise in current beyond this point.

• Label axes: Voltage (V), Current (A).
• Resistor: straight line through origin.
• Filament lamp: curve flattening at higher voltages.
• Diode: near zero current until threshold voltage, then sharp increase.

Resistance (R) is a measure of how much a conductor opposes the flow of electric current. It is measured in ohms (Ω). When a potential difference (voltage) is applied across a conductor, the current that flows depends on the resistance according to Ohm's law (V = IR).

Resistance arises because free electrons moving through the metal collide with fixed ions in the lattice, losing energy and slowing down. The more collisions, the higher the resistance.

• Resistance is measured in ohms (Ω).
• It quantifies opposition to current flow.
• Caused by collisions between electrons and metal ions.

The resistance of a metallic conductor is directly proportional to its length (L). This means that if the length of the conductor doubles, its resistance also doubles.

Physically, a longer wire means electrons have to travel a greater distance through the metal lattice, encountering more ions and thus more collisions, increasing resistance.

Mathematically, this is expressed as: R ∝ L, or R = ρ (L/A), where ρ is the resistivity and A is the cross-sectional area (explained in the next section).

• Resistance increases as length increases.
• Doubling length doubles resistance.
• Longer path means more collisions for electrons.

Resistance is inversely proportional to the cross-sectional area (A) of the conductor. This means that if the cross-sectional area doubles, the resistance halves.

A larger cross-sectional area provides more pathways for electrons to flow, reducing the overall resistance.

Mathematically, this is expressed as: R ∝ 1/A, or R = ρ (L/A).

• Resistance decreases as cross-sectional area increases.
• Doubling area halves resistance.
• More area means more paths for current.

Combining the two proportionalities, resistance is proportional to length divided by cross-sectional area: R ∝ L/A.

The constant of proportionality is called resistivity (ρ), a property of the material, measured in ohm metres (Ω·m).

The full formula is: R = ρ (L/A). Resistivity depends on the material and temperature but is constant for a given material at a fixed temperature.

• Resistance formula: R = ρ (L/A).
• Resistivity ρ is material-dependent, units Ω·m.
• Formula allows calculation of resistance from dimensions and material.

Example: Calculate the resistance of a copper wire 2.0 m long with a cross-sectional area of 1.0 mm². The resistivity of copper is 1.7 × 10⁻⁸ Ω·m.

Step 1: Convert area to m²: 1.0 mm² = 1.0 × 10⁻⁶ m².

Step 2: Use formula R = ρ (L/A) = (1.7 × 10⁻⁸) × (2.0) / (1.0 × 10⁻⁶) = 3.4 × 10⁻² Ω = 0.034 Ω.

• Convert units carefully.
• Substitute values into R = ρ (L/A).
• Calculate and express answer with correct units.