COMMUNICATION

1. Sensing:

• a) Describe and explain:

• I) Current as the Flow of Charged Particles
• Definition:
• Electric current (I) is the flow of charged particles (electrons or ions) through a conductor.
• Mathematically:
• [math]I = \frac{Q}{t}[/math]
• Where Q is the charge in coulombs, and t is time in seconds.
• 
• Figure 1 Flow of charge
• Mechanism:
• In metals, current is carried by free electrons.
• In ionic solutions (electrolytes), current is carried by positive and negative ions.
• Units:
• Current is measured in amperes (A), where [math]1A = \frac{1C}{s}[/math] .
• II) Potential Difference as Energy per Unit Charge
• Definition:
• Potential difference (V) is the energy transferred per unit charge between two points in a circuit.
• Mathematically:
• [math]V = \frac{W}{Q}[/math]
• Where W is the work done (or energy transferred) in joules, and Q is the charge in coulombs.
• Explanation:
• When a charge moves through a component, potential difference measures how much energy it gains or loses.
• Units:
• Potential difference is measured in volts (V), Where [math]1V = \frac{1J}{C}[/math].
• III) Resistance and Conductance, Including Series and Parallel Combinations
• ⇒ Resistance (R):
• Resistance is the opposition to the flow of electric current in a conductor.
• Mathematically:
• [math]R = \frac{V}{I}[/math]
• Where V is potential difference, and I is current.
• 
• Figure 2 Resistance
• ⇒ Conductance (G):
• Conductance is the reciprocal of resistance, indicating how easily current flows:
• [math]G = \frac{1}{R}[/math]
• Conductance is measured in siemens (S).
• 
• Figure 3 Conductance
• ⇒ Series Combination:
• Total resistance:
• [math]R_{\text{total}} = R_1 + R_2 + R_3 + \dots[/math]
• Current is the same through all components.
• 
• Figure 4 Series combination
• ⇒ Parallel Combination:
• Total resistance:
• [math]\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots[/math]
• Potential difference across each branch is the same.
• 
• Figure 5 Parallel combination
• IV) The Effect of Internal Resistance and the Meaning of E.M.F.
• ⇒ Electromotive Force (E.M.F.):
• The total energy supplied by a source per unit charge.
• Mathematically:
• [math]E.M.F.(ε)=W/Q[/math]
• ⇒ Internal Resistance:
• Real batteries and power supplies have internal resistance (r).
• The total voltage across the external circuit (V) is:
• [math]V=ε-Ir[/math]
• Where I is the current.
• 
• Figure 6 Internal resistance
• V) Dissipation of Power in Electric Circuits
• Power (P):
• The rate at which electrical energy is converted into heat or work.
• Mathematically:
• [math]P = VI[/math]
• Using
• [math]V=IR \\
  P=I^2 R  \ or  \ P=V^2/R[/math]
• Dissipation:
• Power dissipated as heat in resistors or other components.
• VI) The Relationship Between Potential Difference and Current in Ohmic Resistors (Ohm’s Law)
• ⇒ Ohm’s Law:
• For an ohmic resistor, the current (I) is directly proportional to the potential difference (V) across it at constant temperature:
• [math]V = IR[/math]
• ⇒ Graph:
• A straight line through the origin on a V–I graph, where the slope equals R.
• 
• Figure 7 V-I graph
• VII) The Action of a Potential Divider
• Definition:
• A potential divider is a circuit that splits an input voltage into smaller output voltages.
• Basic Formula:
• For two resistors ([math]R_1[/math] and [math]R_2[/math]) in series:
• [math]V_{\text{out}} = \frac{R_2}{R_1+R_2} \times V_{\text{in}}[/math]
• Applications:
• Used to adjust voltages in circuits (e.g., volume controls, light sensors).
• VIII) Simple Electrical Behavior of Metals, Semiconductors, and Insulators
• Metals:
• High conductivity due to a large number of free electrons.
• Number density of charge carriers (n) is very high.
• Semiconductors:
• Moderate conductivity.
• n increases with temperature due to thermal excitation of electrons.
• Insulators:
• Extremely low conductivity.
• Very few mobile charge carriers.
• 
• Figure 8 Metal, semiconductor and conductor
• IX) Conservation of Charge and Energy
• Conservation of Charge:
• The total charge in a closed system remains constant.
• Current entering a junction equals current leaving:
• [math]I_{\text{in}} = I_{\text{out}}[/math]
• ​Conservation of Energy:
• In a closed loop, the total energy supplied equals the total energy dissipated:
• [math]\sum E.M.F.s = \sum \text{Potential drops}[/math]

• b) Make appropriate use of:

• I) Explanation and Appropriate Use of Terms
• 1. Electromotive Force (E.M.F.):
• Definition:E.M.F. (ε) is the energy supplied by a source per unit charge when no current flows.
• [math]\varepsilon = \frac{W}{Q}[/math]
• Units: Volts (V).
• Use in Circuits: It represents the maximum voltage provided by a battery or power source, which decreases when internal resistance causes a drop.
• 2. Potential Difference (V):
• Definition: The energy per unit charge transferred between two points in a circuit.
• [math]V = \frac{W}{Q}[/math]
• – Units: Volts (V).
• – Use in Circuits: It measures the energy used by a component (e.g., a resistor or motor).
• 3. Current (I):
• Definition: The flow rate of electric charge through a conductor.
• [math]I = \frac{Q}{t}[/math]
• Units: Amperes (A).
• Use in Circuits: Determines how much charge flows through a circuit in a given time.
• 4. Charge (Q):
• Definition: The property of matter that causes it to experience a force in an electric field.
• [math]Q = I.t[/math]
• Units: Coulombs (C).
• Use in Circuits: Represents the amount of electric charge moved through the circuit.
• 5. Resistance (R):
• Definition: The opposition to current flow in a conductor.
• [math]R = \frac{V}{I}[/math]
• ​Units: Ohms (Ω).
• Use in Circuits: Determines the potential difference required for a given current.
• 6. Conductance (G):
• Definition: The ease with which current flows, reciprocal of resistance.
• [math]G = \frac{1}{R}[/math]
• – Units: Siemens (S).
• – Use in Circuits: Used to evaluate how efficiently a material conducts current.
• 7. Series Circuits:
• – Definition: Components connected end-to-end, with the same current passing through each.
• [math]R_{\text{total}} = R_1 + R_2 + R_3 + \dots[/math]
• – Use in Circuits: Used when components need equal current (e.g., string lights).
• 8. Parallel Circuits:
• Definition: Components connected across the same potential difference.
• [math]\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots[/math]
• Use in Circuits: Allows multiple pathways for current; used in home wiring.
• 9. Internal Resistance (r):
• Definition: The inherent resistance inside a power source (e.g., a battery).
• Use in Circuits: Causes a voltage drop:
• [math]V = \varepsilon – Ir[/math]
• 10. Load:
• Definition: The external components or devices connected to a circuit (e.g., resistors, motors).
• Use in Circuits: Determines how much power the source must supply.
• 11. Resistivity (ρ):
• Definition: A material’s intrinsic property that opposes current flow.
• [math]\rho = \frac{R \cdot A}{L}[/math]
• Units: Ohm meters (Ω.m).
• Use in Circuits: Used to compare materials’ suitability for specific applications.
• 12. Conductivity (σ):
• Definition: Reciprocal of resistivity, indicating how well a material conducts current.
• [math]\sigma = \frac{1}{\rho}[/math]
• – Units: Siemens per meter (S/m).
• 13. Charge Carrier Number Density (n):
• Definition: The number of charge carriers (e.g., electrons) per unit volume in a material.
• – Relation to Current:
• [math]I=nqvA[/math]
• Where:
• – n: Charge carrier density.
• – q: Charge of a single carrier.
• – v: Drift velocity.
• – A: Cross-sectional area.
• II) Recognizing Standard Circuit Symbols
• Below are common circuit symbols:
• Resistor:
• – A rectangle
• Battery:
• – A series of short and long parallel lines.
• Switch:
• – A breakable line with a pivot.
• Ammeter:
• – A circle with an “A.”
• Voltmeter:
• – A circle with a “V.”
• Diode:
• – A triangle pointing toward a line.
• 
• Figure 9 Circuit symbol
• III) Sketching and Interpreting Graphs
• 1. Graph of Current Against Potential Difference
• ⇒ Ohmic Resistors (Ohm’s Law):
• Graph: A straight line through the origin.
• Interpretation:
• – The slope (1/R) is constant.
• – Current is directly proportional to potential difference.
• ⇒ Non-Ohmic Devices:
• Graph: A curve (non-linear relationship).
• Examples:
• – Filament Lamp: Resistance increases with temperature, causing the curve to flatten.
• – Diode: Conducts only in one direction, showing negligible current in reverse bias.
• 
• Figure 10 (a) non-Ohmic (b) Ohmic graph
• 2. Graph of Resistance or Conductance Against Temperature
•  Metals:
• Resistance: Increases with temperature due to increased collisions of electrons with lattice ions.
• Graph: Linear increase.
• 
• Figure 11 Graph between temperature and resistivity between different components
• Semiconductors:
• Conductance: Increases with temperature due to excitation of more charge carriers.
• Graph: Exponential rise.
• Insulators:
• Conductance: Minimal at lower temperatures but may increase at very high temperatures.

• c) Make calculations and estimates involving:

• 1. Ohm’s Law and Conductance
• Ohm’s Law relates voltage, current, and resistance in an electrical circuit:
• Resistance R: ​[math]R = \frac{V}{I}[/math]
• – V: Voltage across the resistor (Volts, V)
• – I: Current through the resistor (Amperes, A)
• – R: Resistance of the conductor (Ohms, Ω)
• Conductance G: [math]G = \frac{I}{V} \quad \text{or} \quad G = \frac{I}{R}[/math]
• – G: Conductance (Siemens, S)
• – High conductance corresponds to low resistance.
• 2. Power and Energy Relationships
• Power (Rate of Energy Transfer):
• The rate at which energy is transferred in a circuit is given by:
• [math]P = IV \quad (\text{Power} = \text{Current} \times \text{Voltage})[/math]
• Other equivalent power expressions using Ohm’s Law:
• [math]P = I^2 R \\
  \text{Substitute } V = IR \text{ into } P = IV \\
  P = \frac{V^2}{R} \\
  \text{Substitute } I = \frac{V}{R} \\
  V = IR \\
  P = \frac{(IR)^2}{R} \\
  P = I^2 R[/math]
• ⇒ Energy Transferred:
• The energy transferred in a circuit over time t is:
• [math]W=VIt[/math]
• – W: Energy transferred (Joules, J)
• – V: Voltage (Volts)
• – I: Current (Amperes)
• – t: Time (Seconds, s)
• 3. Internal Resistance and Electromotive Force (emf):
• For a source of emf ε with internal resistance[math]r_{\text{internal}}[/math] ​:
• Terminal Voltage V:
• [math]V = \varepsilon – I r_{\text{internal}}[/math]
• – [math]\varepsilon[/math]: Electromotive force (Volts)
• – [math]r_{\text{internal}}[/math]: Internal resistance of the source (Ohms, Ω)
• Key Insight: As current I increase, the voltage drop across the internal resistance increases, reducing the terminal voltage V.
• 4. Charge and Current Relationship
• – Current I:
• [math]I = \frac{\Delta W}{\Delta Q}[/math]
• – [math]\Delta W[/math]​: Work done or energy transferred (Joules, J)
• – [math]\Delta Q[/math]: Electric charge (Coulombs, C)
• Charge Flow:
• [math]Q = It[/math]
• If current I flows for time t, the total charge transferred is Q.
• 5. Resistance and Conductance in Series and Parallel Circuits
• Resistors in Series (Same Current):
• [math]R_{\text{total}} = R_1 + R_2 + R_3 + \dots[/math]
• – Total resistance is the sum of individual resistances.
• Resistors in Parallel (Same Voltage):
• [math]\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots[/math]
• – Total resistance [math]R_{\text{total}}[/math]​ is less than the smallest individual resistance.
• Conductance in Parallel (Direct Sum):
• [math]G_{\text{total}} = G_1 + G_2 + G_3 + \dots[/math]
• Conductance in Series:
• [math]\frac{1}{G_{\text{total}}} = \frac{1}{G_1} + \frac{1}{G_2} + \frac{1}{G_3} + \dots[/math]
• 6. Resistivity and Conductivity
• Resistance of a Material:
• [math]R = \rho \frac{L}{A}[/math]
• – [math]\rho[/math]: Resistivity of the material (Ohm-meters, Ω·m)
• – L: Length of the conductor (meters, m)
• – A: Cross-sectional area of the conductor (m²)
• Conductance of a Material:
• [math]G = \sigma \frac{A}{L}[/math]
• – [math]\sigma[/math]Conductivity of the material (Siemens per meter, S/m)
• – High resistivity implies low conductivity and vice versa.
• 7. Potential Divider Circuit:
• A potential divider splits an input voltage [math]V_{\text{in}}[/math] into smaller voltages.
• Output Voltage [math]V_{\text{out}}[/math]​:
• – Using two resistors [math]R_1[/math] and [math]R_2[/math] ​:
• [math]V_{\text{out}} = \frac{R_2}{R_1+R_2} \cdot V_{\text{in}}[/math]
• – [math]V_{\text{out}}[/math]​: Voltage across [math]R_2[/math]
• – [math]V_{\text{in}}[/math]​: Input voltage
• ⇒ Ratio of Voltages (Voltage Divider Rule):
• The voltage across two resistors is proportional to their resistances:
• [math]\frac{V_1}{V_2} = \frac{R_1}{R_2}[/math]
• – [math]V_1[/math]​: Voltage across [math]R_1[/math]​​
• – [math]V_2[/math]​: Voltage across [math]R_2[/math]​
• o Applications:
• – Used to reduce voltage levels in circuits.
• – Provides reference voltages for sensors or op-amps.

• ⇒ Example Calculation (Potential Divider):
• If [math]V_{\text{in}} = 12V, \quad R_1 = 4\Omega, \quad R_2 = 4\Omega[/math]:
• [math]V_{\text{out}} = \frac{R_2}{R_1+R_2} \cdot V_{\text{in}} \\
  V_{\text{out}} = \frac{8}{4+8} \cdot 12 = 8V[/math]
• The voltage across [math]R_2[/math] is 8V.

•  d) Demonstrate and apply knowledge and understanding of the following practical activities (HSW4):

• I. Investigating Electrical Characteristics for Ohmic and Non-Ohmic Components
• Objective:
• – To investigate how voltage (V) and current (I) behave in ohmic and non-ohmic components and determine their characteristics.
• Theory:
• Ohmic Components (e.g., resistors):
• – Follow Ohm’s Law: V = IR
• – The V-I graph is a straight line through the origin (constant resistance).
• Non-Ohmic Components (e.g., filament lamp, diode, thermistor):
• – Do not follow Ohm’s Law.
• – Resistance changes with voltage or current. The V-I graph is nonlinear.
• Apparatus:
• – Power supply (variable DC supply)
• – Voltmeter (to measure V)
• – Ammeter (to measure I)
• – Resistor, filament lamp, diode, or thermistor
• – Connecting wires
• – Rheostat (to vary the current)
• Method:
• – Set up the circuit: Power supply → component → ammeter → back to power supply.
• – Connect the voltmeter in parallel across the component.
• – Gradually increase the voltage using the power supply or a rheostat.
• – Record the corresponding values of current (I) and voltage (V) at regular intervals.
• – Plot a graph of V against I.
• Analysis:
• – For ohmic components (e.g., resistor):
• The graph is a straight line. The gradient gives the resistance:
• [math]R =  \frac{V}{I}[/math]
• For non-ohmic components (e.g., filament lamp):
• – The curve bends because resistance increases as temperature rises.
• – For a diode: Current flows only when V exceeds a threshold (forward bias).
• – For a thermistor: Resistance decreases as temperature increases.
• II. Determining the Resistivity or Conductivity of a Metal
• Objective:
• To determine the resistivity (ρ) or conductivity (σ) of a metal wire.
• Theory:
• The resistance R of a wire depends on:
• [math]R = \rho \frac{L}{A} \quad \text{or} \quad G = \sigma \frac{A}{L}[/math]
• – ρ: Resistivity of the metal (Ohm-meters,[math]\Omega \cdot m[/math])
• – σ: Conductivity (S/m, Siemens per meter)
• – L: Length of the wire (m)
• – A: Cross-sectional area ([math]m^2[/math])
• Apparatus:
• – Wire (of known material)
• – Power supply
• – Ammeter and voltmeter
• – Micrometer screw gauge (to measure wire diameter)
• – Ruler (to measure length)
• Method:
• – Measure the length L of the wire accurately using a ruler.
• Measure the diameter d of the wire using a micrometer at several points and calculate the cross-sectional area:
• [math]A = \frac{\pi d^2}{4}[/math]
• – Set up a circuit with the wire as the resistor. Connect the voltmeter in parallel and the ammeter in series.
• – Gradually vary the voltage and record the current and voltage readings.
• – Calculate resistance (R) for each voltage-current pair using [math]R = \frac{V}{I}[/math]​.
• – Plot R against [math] \frac{L}{A}[/math]​. The gradient of the line gives resistivity:
• [math]\rho = \text{Gradient of } R \text{ vs. } \frac{L}{A}[/math]
•    o     Conductivity (σ):
• [math]\sigma = \frac{1}{\rho}[/math]
• III. Use of Potential Divider Circuits with Sensors (e.g., Thermistor, LDR)
• Objective:
• o To use a potential divider circuit to vary output voltage (​[math]V_{\text{out}}[/math]) based on external conditions.
• Theory:
• o A potential divider splits input voltage (​[math]V_{\text{in}}[/math]) into smaller voltages. Using resistors [math]R_1[/math] and [math]R_2[/math] :
• [math]V_{\text{out}} = \frac{R_2}{R_1+R_2} \cdot V_{\text{in}}[/math]
• o A thermistor (temperature-dependent resistor): Resistance decreases as temperature increases.
• o A Light-Dependent Resistor (LDR): Resistance decreases as light intensity increases.
• Apparatus:
• – Power supply
• – Thermistor or LDR
• – Fixed resistor
• – Voltmeter
• Method:
• – Set up the potential divider circuit: Power supply →[math]R_1[/math] and [math]R_2[/math]​ in series → back to power supply.
• – Place the thermistor/LDR as ​[math]R_2[/math]. Connect the voltmeter across [math]R_2[/math].
• – Vary the external condition (temperature for thermistor or light intensity for LDR).
• – Record [math]V_{\text{out}}[/math]​ for different conditions.
• Applications:
• – Thermistors in thermostats.
• – LDRs in automatic lighting systems.
• IV. Calibration of a Sensor or Instrument
• Objective:
• To calibrate a sensor (e.g., thermistor or LDR) to relate its output to a specific condition (e.g., temperature or light intensity).
• Method:
• – Place the sensor (thermistor or LDR) in known, measurable conditions (e.g., a water bath for temperature).
• – Record the sensor’s output voltage [math]V_{\text{out}}[/math] at each condition.
• – Plot a calibration curve of [math]V_{\text{out}}[/math]​ against the condition (e.g., temperature or light intensity).
• – Use the graph to determine unknown conditions based on [math]V_{\text{out}}[/math].
• Example:
• – For a thermistor, the graph might show a nonlinear decrease in voltage with increasing temperature.
• V. Determining the Internal Resistance of a Chemical Cell
• Objective:
• To measure the internal resistance (r) of a cell.
• Theory:
• The terminal voltage V of a cell is given by:
• [math]V = \varepsilon – I r[/math]
• Where:
• – ε: Emf (open circuit voltage)
• – r: Internal resistance of the cell
• – I: Current through the circuit
• Apparatus:
• – Cell (source of emf)
• – Variable resistor (to change current)
• – Voltmeter and ammeter
• Method:
• – Connect the cell to a circuit with a variable resistor, ammeter, and voltmeter.
• – Adjust the variable resistor to change the current I.
• – Record the corresponding terminal voltage V for each current.
• – Plot V against I.
• Analysis:
• – The graph of V vs I is a straight line:
• [math]V = \varepsilon – I r[/math]
• – The y-intercept gives ε (emf).
• – The gradient gives -r  (negative internal resistance).