Electrical quantities
Charges and Forces
There are two types of electric charge: positive and negative. Like charges repel each other, while opposite charges attract. This fundamental rule explains why positive charges repel other positive charges, negative charges repel other negative charges, but positive charges attract negative charges.
Production of Electrostatic Charges
Electrostatic charges are produced by friction. When two different insulating materials are rubbed together, electrons are transferred from one material to the other. The material that gains electrons becomes negatively charged; the material that loses electrons becomes positively charged. This is because charging by friction involves only the transfer of negative charge (electrons), not positive charge.
Detection and Conduction
To detect electrostatic charges, we use an electroscope. A charged object brought near the metal plate induces a charge separation in the electroscope's internal leaves, causing them to diverge. To distinguish between conductors and insulators, we can observe how quickly a charged electroscope discharges when touched by different materials. Conductors allow charge to flow easily, while insulators do not.
Conductors vs. Insulators
Using a simple electron model:
- Conductors (e.g., metals): Contain 'free electrons' that are not bound to specific atoms and can move freely through the material. This allows charge to flow.
- Insulators (e.g., plastic, rubber): Electrons are tightly bound to their atoms and cannot move freely. Charge remains localized.
An electric field is a region in which an electric charge experiences a force. The direction of the electric field at any point is defined as the direction of the force that would act on a positive charge placed at that point.
Field Patterns:
- Around a point charge: Radial lines pointing outwards (for positive) or inwards (for negative).
- Around a charged conducting sphere: Same as a point charge located at the center; radial lines.
- Between two oppositely charged parallel plates: Uniform field with straight, parallel, equally spaced lines pointing from the positive plate to the negative plate.
Correction: Only electrons (negative charge) move. Positive charges (protons) are fixed in the nucleus and do not transfer.
Why examiners accept this: The definition must explicitly mention the force experienced by a charge. Simply saying 'a region with charge' is insufficient because charges exist without fields in static equilibrium contexts, but a field implies the potential for force.
Example phrase: "A region where an electric charge experiences a force."
Electric Current
Electric current is the flow of charge. In metals, this is due to the movement of free electrons. The direction of conventional current is defined as flowing from positive to negative. However, the actual flow of free electrons is from negative to positive.
Types of Current:
- Direct Current (d.c.): Charge flows in one constant direction (e.g., from a battery).
- Alternating Current (a.c.): The direction of charge flow reverses periodically (e.g., mains supply).
Measuring Current
An ammeter is used to measure current. It must be connected in series with the component.
- Analogue ammeters: Require careful reading of the scale to avoid parallax error. Select a range where the deflection is large but within the scale for accuracy.
- Digital multimeters: Often auto-range, but manual selection may be needed. Ensure the range is appropriate to avoid overloading.
Electric current is defined as the charge passing a point per unit time.
Equation: I = \frac{Q}{t}
Where:
- I = current in amperes (A)
- Q = charge in coulombs (C)
- t = time in seconds (s)
Equation: E = \frac{W}{Q}
Potential Difference (p.d., V): The work done by a unit charge passing through a component.
Equation: V = \frac{W}{Q}
Where:
- E or V = e.m.f. or p.d. in volts (V)
- W = work done (energy transferred) in joules (J)
- Q = charge in coulombs (C)
Note: In these equations, E is used for Electromotive Force to distinguish it from Energy (also often denoted as E or W). Context usually clarifies which is meant, but remember V is specifically for p.d. across a component.
A voltmeter measures potential difference. It must be connected in parallel across the component being measured.
- Analogue voltmeters: Read the scale carefully; select a range that gives a large deflection for precision.
- Digital multimeters: Ensure correct input jacks and range selection to avoid damage or inaccurate readings.
Correction: Conventional current is positive to negative. Electron flow is negative to positive. They are opposite directions.
Why examiners accept this: They look for the correct substitution into E = W/Q or V = W/Q. Ensure units are consistent (Joules and Coulombs).
Example phrase: "The e.m.f. is the work done per unit charge."
Resistance (R)
Resistance is the ratio of potential difference to current.
Equation: R = \frac{V}{I}
Where:
- R = resistance in ohms (\Omega)
- V = potential difference in volts (V)
- I = current in amperes (A)
Factors Affecting Resistance of a Wire:
- Length: Resistance is directly proportional to length (R \propto l). Longer wire = more resistance.
- Cross-sectional Area: Resistance is inversely proportional to cross-sectional area (R \propto 1/A). Thicker wire = less resistance.
I-V Graphs (Current-Voltage Characteristics):
- Resistor (constant temperature): Straight line through the origin. Constant resistance.
- Filament Lamp: Curve flattening at higher voltages. Resistance increases as the filament heats up.
- Diode: Current flows only in one direction (forward bias). Negligible current in reverse bias.
Aim: To determine the resistance of a component.
Apparatus: Power supply, ammeter, voltmeter, component, variable resistor (rheostat), connecting wires.
Circuit Setup:
- Connect the power supply, ammeter, and component in series.
- Connect the voltmeter in parallel across the component.
- Connect the variable resistor in series to vary the current.
Procedure:
- Close the switch and record the readings of current (I) and potential difference (V).
- Adjust the variable resistor to change the voltage and current.
- Record at least 5 pairs of V and I values.
Calculation:
- Calculate resistance for each pair using R = V/I.
- Find the average resistance, OR plot a graph of V (y-axis) against I (x-axis) and find the gradient.
Correction: Resistance is inversely proportional to the cross-sectional area. Since Area A = \pi (d/2)^2, resistance is inversely proportional to the square of the diameter (R \propto 1/d^2).
Why examiners accept this: They look for the correct shape and explanation of why it curves. For a lamp, mention temperature increase. For a diode, mention unidirectional flow.
Example phrase: "The curve flattens because resistance increases as the filament gets hotter."
Electric circuits transfer energy from a source (cell/mains) to components and then into the surroundings (heat, light, etc.).
Power (P)
Power is the rate of energy transfer.
Equation: P = I \times V
Where:
- P = power in watts (W)
- I = current in amperes (A)
- V = potential difference in volts (V)
Energy (E)
Equation: E = I \times V \times t
Where:
- E = energy in joules (J)
- t = time in seconds (s)
Kilowatt-hour (kWh)
The kWh is a unit of energy used for billing. It is the energy transferred by a 1 kW appliance running for 1 hour.
Cost calculation: Cost = Power (kW) \times Time (h) \times Price per kWh.
Conversion: 1 \text{ kWh} = 1000 \text{ W} \times 3600 \text{ s} = 3,600,000 \text{ J}.
Correction: Always convert power to Watts and time to seconds when calculating Joules. For kWh, use kW and hours.
Why examiners accept this: They check for correct unit conversion (W to kW) and time (h).
Example phrase: "Energy = Power (kW) \times Time (h). Cost = Energy \times Rate."