Comprehensive Notes on Current Electricity and Magnetism

Current Electricity

• Current (I): The flow of charges in a circuit, measured in Amperes (A) and milli amperes (mA).

• Conventional Current Direction: Positive to negative.

• Electron Flow: Negative to positive.

Quantifying Current

• Current is the rate of charge flow.

• The more charges passing through a wire in one second, the bigger the current.

• Formula: $Q = I \times t$, where:

  • Q = Charge (in Coulombs)

  • I = Current (in Amperes)

  • t = Time (in seconds)

• $I = \frac{Q}{t}$

• Ammeter: An instrument to measure electric current flowing in a circuit, symbol: (Ammeter symbol).

Example Questions

• Question 1:

  • In 10 seconds, 60 C of charge flows around the circuit.

  • Calculate the current.

  • Solution: $I = \frac{Q}{t} = \frac{60}{10} = 6A$

• Question 2:

  • A current of 150 mA flows around a circuit for 3 minutes.

  • How much electric charge flows around the circuit in this time?

  • Solution:

    • Convert time to seconds: $3 \times 60 = 180$ seconds

    • Convert current to Ampere: $150 / 1000 = 0.15$ A

    • $Q = I \times t = 0.15 \times 180 = 27$ C

Electromotive Force (e.m.f.)

• Measured by the energy dissipated by a source (battery) in driving a unit charge around a complete circuit.

• The energy supplied to each coulomb of charge within it.

• Formula: $ε = \frac{E}{Q}$, where:

  • ε = Electromotive force (e.m.f)

  • E = Energy supplied by the cell

  • Q = Charges flow through the cell

• e.m.f = workdone / charge

• Unit: J/C or Volt (V)

Potential Difference (p.d) or Voltage

• Energy carried by charges is consumed in components (resistance, lamp, heater).

• When charges flow through lamps, their energy is converted into heat and light.

• The energy converted per unit charge passing through a component.

• Formula: $p.d = \frac{E}{Q}$

• The unit of potential difference is volt (V)

• Voltmeter: Used to measure potential difference across a component.

Resistance (R)

• The resistance of a component is measured in Ohm ($\Omega$).

• Formula: $R = \frac{V}{I}$, where:

  • R = Resistance

  • V = Potential difference

  • I = Current

Worked Example

• A resistor connected in a circuit has a current of 2 A and a voltage of 15 V.

• Calculate the resistance.

• Solution: $R = \frac{V}{I} = \frac{15}{2} = 7.5 \Omega$

Measuring Resistance

• Connect an electrical component or conducting wire in series with a battery and ammeter.

• Connect the voltmeter parallel to the electrical component or wire.

• Measure the voltmeter and ammeter readings.

• Calculate resistance using the formula: $R = \frac{V}{I}$

Factors Affecting Resistance

• Length of Wire:

  • Resistance is proportional to the length of the wire.

  • Longer wire = greater resistance (more collisions with metal ions).

• Cross-sectional Area:

  • Resistance is inversely proportional to the cross-sectional area.

  • Greater area = lower resistance (more electrons available to carry charge).

• Temperature:

  • Metallic wires: As temperature increases, resistance increases.

  • Semiconductors (silicon, germanium): As temperature increases, resistance decreases.

• Material:

  • Copper: Good conductor, used for connecting wires.

  • Nichrome: Higher resistance, used in heating elements.

Electric Power

• Rate at which work is done or energy is transformed in an electrical circuit.

• Measure of how much energy is used in a span of time.

• Symbol: P

• SI Unit: Watt, joule per second

• Scalar quantity

• Formula: $P = VI$, where:

  • P = Power

  • V = Potential difference

  • I = Electric current

Magnetic Field

• Tool to describe how magnetic force is distributed in space around and within something magnetic.

Properties of Magnetic Field

• Magnetic field lines never cross.

• Field lines bunch together where the magnetic field is strongest (density indicates strength).

• Field lines make closed loops (continue inside a magnetic material).

• Arrowheads indicate the direction of the field (from North to South).

• 'N' and 'S' labels are placed on the ends of a magnetic field source.

Magnetic Materials

• Materials that attract magnets and can be magnetized.

• Examples: iron, steel, cobalt, nickel, etc.

Non-Magnetic Materials

• Materials that do not attract magnets.

• Examples: brass, copper, zinc, tin, aluminum, non-metals.

Magnetized Materials

• Materials that act as magnets and have all magnetic properties.