Electricity, Current, Potential Difference and Resistance

Electricity Current, Potential Difference, and Resistance

Current as the Rate of Flow of Charge

  • Current is analogous to the flow of water in a pipe, dependent on flow rate and time.

  • Measured using an ammeter in series with the circuit component.

  • Defined mathematically as: I = \frac{\Delta Q}{\Delta t}, where:

    • \Delta Q is the charge in coulombs (C).

    • I is the current in amperes (A).

    • \Delta t is the time taken in seconds (s).

  • One coulomb (C) is the amount of charge that passes in 1 second when the current is 1 ampere (A).

  • Conventional current flows from + to -, opposite to electron flow.

Potential Difference as Energy per Unit Charge

  • Electric charge flow requires work.

  • Potential Difference (p.d.) or voltage is defined as work done per unit charge moved.

  • Example: Doing 6 J of work moving 1 C of charge through a resistor results in a p.d. of 6 V, converting energy to heat.

  • Potential difference is like the pressure forcing water along a pipe.

  • Definition of the Volt: The potential difference across a component is 1 volt when 1 joule of energy is converted moving 1 coulomb of charge through the component.

    • 1 V = 1 J C^{-1}

  • Formula: V = \frac{W}{Q}, where

    • V is potential difference in volts (V).

    • W is work done (energy converted) in joules (J).

    • Q is charge in coulombs (C).

  • Measured using a voltmeter in parallel with the component.

  • Potential difference across components in parallel is the same.

Resistance

  • When a potential difference is applied across a component, a current flows.

  • The amount of current depends on the component's resistance.

  • Resistance measures how difficult it is for a current to flow through a component.

  • Mathematically defined as: R = \frac{V}{I}, where:

    • V is potential difference in volts (V).

    • I is current in amperes (A).

    • R is resistance in ohms ((\Omega)).

  • Resistance is measured in ohms ((\Omega)).

  • A component has a resistance of 1 (\Omega) if a potential difference of 1 V causes a current of 1 A to flow through it.

Assumptions

  • Voltmeters are assumed to have infinite resistance.

  • Ammeters are assumed to have no resistance.

Ohm's Law and Ohmic Conductors

  • Ohm's Law relates current and potential difference for certain conductors.

  • Ohmic conductors (mostly metals) obey Ohm's Law.

  • For an Ohmic Conductor, R is constant.

  • The current is directly proportional to the potential difference, provided physical conditions like temperature remain constant. \ I \propto V

  • Ohm’s law is only true for ohmic conductors under constant physical conditions (e.g., temperature).

I/V Characteristics

  • I/V characteristic is a graph of I against V, showing how current changes with potential difference.

Ohmic Conductor

  • At constant temperature, the current is directly proportional to voltage.

  • The I/V graph is a straight line through the origin.

  • Steeper gradients indicate lower resistance, whether plotting I/V or V/I.

Filament Lamp

  • The I/V characteristic is a curve that gets shallower as the voltage rises.

  • The filament's temperature increases with current, increasing resistance.

  • The V/I graph is a curve that gets steeper as the current and voltage increase

Semiconductors and Sensors

  • Semiconductors have fewer charge carriers than metals.

  • Energy supplied to a semiconductor releases more charge carriers.

  • Excellent for detecting environmental changes.

Diodes

  • Allow current flow in one direction only (forward bias).

  • Require a threshold voltage (about 0.6 V) in the forward direction to conduct.

  • In reverse bias, resistance is very high, and current is tiny.

  • Circuit symbols: Diode and LED.

  • Current flows in the direction that the triangle in the circuit symbol points.

Thermistors

  • Resistors with resistance depending on temperature.

  • NTC (Negative Temperature Coefficient) thermistors' resistance decreases as temperature rises.

  • Warming the thermistor releases more charge carriers, lowering resistance.

  • The I/V characteristic graph curves upwards, indicating decreasing resistance with increasing current.

Resistivity

  • Length (l): Longer wire means higher resistance.

  • Area (A): Wider wire means lower resistance.

  • Resistivity ((\rho)): A material property affected by environmental factors (e.g., temperature, light intensity).

  • The resistivity of a material is defined as the resistance of a 1 m length with a 1 m^2 cross-sectional area.

  • It is measured in ohm-metres ((\Omega)m).

  • Formula: \rho = \frac{RA}{l}, where:

    • \rho (rho) is resistivity.

    • R is resistance.

    • A is cross-sectional area.

    • l is length.

Calculating Resistivity of a Wire

  • Assume the wire is cylindrical with a circular cross-section.

  • Use A = \pi r^2 to find the cross-sectional area.

  • Measure the diameter at multiple points using a micrometer, average the values, and divide by 2 to obtain the radius r in meters.

  • Calculate resistance using R = \frac{V}{I}.

Practical Skills

  • Clamp test wire to a ruler, starting at zero.

  • Attach flying lead with crocodile clip to the wire.

  • Measure the length, voltage, and current.

  • Calculate resistance using R=\frac{V}{I}.

  • Repeat measurements and calculate the gradient of the line of best fit.

  • Calculate the resistivity using the relationship \\ R = \frac{\rho l}{A}, so multiply the gradient of the line of best fit with the cross-sectional area of the wire to find the resistivity.

Superconductivity

  • Superconductors have zero resistivity below a transition temperature.

  • No electrical energy is converted to heat.

  • Applications: Power cables, strong electromagnets, fast electronic circuits.

Power as the Rate of Transfer of Energy

  • Power is defined as the rate of transfer of energy, measured in watts (W).

  • P = \frac{E}{t}, where:

    • P is power in watts (W).

    • E is energy in joules (J).

    • t is time in seconds (s).

  • Using V = IR

  • Combining the two equations gives you loads of different ways to calculate power.

  • \P = VI

  • \P = I^2R

  • P = \frac{V^2}{R}

Electrical Energy

  • E = VIt

  • E = \frac{V^2}{R}t

  • E= I^2Rt

EMF and Internal Resistance

  • Batteries have internal resistance (r) due to collisions within the battery.

  • Electromotive Force (EMF, E) is the energy per coulomb supplied by the source, measured in volts.

  • Terminal Potential Difference (V) is the energy transferred per coulomb in the load resistance (R).

  • Lost Volts (v) is the energy wasted per coulomb overcoming the internal resistance.

  • To find the EMF of cells in series, the total EMF is equal to the sum of the EMFs. E{total} = E1 + E2 + E3 + …

  • To find the EMF of cells in parallel, the total EMF for the parallel branches is equal. E{total} = E1 = E2 = E3 = …

  • Formulae:

    • \epsilon = V + v

    • \epsilon = I(R + r)

    • V = \epsilon Ir

Conservation of Energy and Charge

  • Kirchhoff’s Second Law: The total EMF around a series circuit equals the sum of p.d.s across each component: E = \sum IR

  • Kirchhoff’s First Law: The total current entering a junction equals the total current leaving it: I{in} = I{out}

  • Series Circuits:

    • Same current at all points.

    • EMF splits: E = V1 + V2 + V_3

    • Total resistance: R{total} = R1 + R2 + R3

  • Parallel Circuits:

    • Current splits: I = I1 + I2 + I_3

    • Same p.d. across all components (separate loops)

    • \frac{1}{R{total}} = \frac{1}{R1} + \frac{1}{R2} + \frac{1}{R3}

Potential Divider

  • A circuit with voltage source and resistors in series.

  • Potential difference across the voltage source is split in the ratio of their resistances.

  • By Ohm's Law,V = IR for each resistor.

  • Allows supplying a fraction of the source voltage, useful for calibrating voltmeters or acting as a voltage supply

  • V{out} = Vs \frac{R2}{R1 + R_2}, where

    • Vs is source voltage

    • R are the resistances of the circuit

Potential Divider with Sensors

  • Using an LDR or Thermistor as one of the resistors produces an output voltage that varies with light level or temperature.

  • Variable resistance depends on light and temperature.

Potentiometer

  • Uses a variable resistor (replacing R1 and R2) to vary voltage (Vout) from 0 V up to source voltage (Vs).

  • Useful for continuously changing voltage, like in a stereo volume control.

The provided note includes the following main topics:

  1. Current as the Rate of Flow of Charge

  2. Potential Difference as Energy per Unit Charge

  3. Resistance

  4. Ohm's Law and Ohmic Conductors

  5. I/V Characteristics

  6. Semiconductors and Sensors

  7. Diodes

  8. Thermistors

  9. Resistivity

  10. Calculating Resistivity of a Wire

  11. Practical Skills

  12. Superconductivity

  13. Power as the Rate of Transfer of Energy

  14. Electrical Energy

  15. EMF and Internal Resistance

  16. Conservation of Energy and Charge

  17. Potential Divider

  18. Potential Divider with Sensors

  19. Potentiometer

The provided note includes the following main topics:

  1. Current as the Rate of Flow of Charge

  2. Potential Difference as Energy per Unit Charge

  3. Resistance

  4. Ohm's Law and Ohmic Conductors

  5. I/V Characteristics

  6. Semiconductors and Sensors

  7. Diodes

  8. Thermistors

  9. Resistivity

  10. Calculating Resistivity of a Wire

  11. Practical Skills

  12. Superconductivity

  13. Power as the Rate of Transfer of Energy

  14. Electrical Energy

  15. EMF and Internal Resistance

  16. Conservation of Energy and Charge

  17. Potential Divider

  18. Potential Divider with Sensors

  19. Potentiometer