Electrical Circuits

Here are five tips to master AQA A Level Physics Electricity:

1. Grasp Key Concepts: Master Ohm’s Law and circuit principles in AQA A Level Physics Electricity.
2. Practice Circuit Analysis: Solve series and parallel circuit problems for AQA A Level Physics Electricity.
3. Master Calculation: Focus on power, energy, and resistance in AQA A Level Physics Electricity.
4. Use Visual Aids: Create diagrams and flowcharts for AQA A Level Physics Electricity.
5. Review Past Papers: Analyze AQA A Level Physics Electricity past papers for common questions.

1. Electrical power in circuits:

• An incredibly intricate work of electronic engineering is the integrated circuit of an iPhone.
• It entails the communication between thousands of tiny electrical components.
• These are made to cooperate in order to regulate the phone’s numerous features.
• Despite their complexity, all of the circuits are founded on a few fundamental concepts and laws of circuitry.
• Integrated circuits are excellent at single-step, basic tasks.
• They merely complete them in predetermined order and extremely swiftly.
• The total power that each individual electrical component in a circuit transfer equals the total power that the circuit transfers.
• A component’s ability to transfer electrical power is determined by the potential difference across it and the current that passes through it. Power is often defined as:
• power = rate of doing work or rate of energy transfer
• or
• [math] P = \frac{\Delta W}{\Delta t}[/math]
• Thus, the rate at which electrical work is completed may be used to describe electrical power in an electrical context.
• A component’s resistance, current, and potential difference may all be utilized to compute the electrical power it transfers.
• This power can be calculated using a variety of formulas.
• [math] \text{Current} = \frac{\text{Charge}}{\text{Time}} [/math]
• In terms of symbols:
• [math] I = \frac{Q}{t} \\ Q = I t \quad \text{(1)} \\ \text{Potential difference} = \frac{\text{Electrical energy}}{\text{Charge}} [/math]
• In terms of symbols:
• [math] V= \frac{W}{Q} \\ Q= \frac{W}{V}[/math]
• Substitute in equation 1
• [math] It =\frac{W}{V} [/math]
• Then
• [math]IV = \frac{W}{t} [/math]
• So,
• [math] P = IV \qquad  (2) [/math]
• By using the Ohm’s law
• [math] V = IR [/math]
• Put in equation 2
• [math] P= I(IR) [/math]
• Then,
• [math] P = I^2 R \qquad (3) [/math]
• If we rearranging the ohm’s equation then we get
  [math] I= \frac{V}{R} [/math]
• Put in equation 3
• [math] P = \left(\frac{V}{R}\right)^2 R \\ P = \frac{V^2}{R^2} \cdot R [/math]
• So,
• [math] P = \frac{V^2}{R}  \qquad (4) [/math]
• In the form of energy
• [math] \text{Power} = \frac{\text{Energy}}{\text{Time}} \\ \text{Energy} = V \cdot I \cdot t [/math]
• The connection P = IV is very helpful because it makes it possible to calculate electrical power using current and potential difference, two quantities that are simple to measure and keep track of.
• Real-time monitoring of a circuit’s electrical power consumption is made possible by data-logging ammeters and voltmeters.
• This enables battery-powered devices, like laptops, tablets, and smartphones, to show their remaining energy and estimate how long they will last before needing to be charged.
• A resistor is a passive electrical component that reduces the voltage or current in a circuit.
• Symbol:
• The symbol for a resistor is a zigzag line or a rectangular box with a “R” inside.
• Units:
• Resistors are measured in Ohms (Ω), with common values ranging from a few ohms to millions of ohms.

2. Circuit calculation:

• The basic functions of current and potential difference in circuits are very important knowledge for electronic engineers.
• The “rules” pertaining to these are all-encompassing and may be applied to both basic circuits and the complex circuits present in integrated circuit chips.
• Kirchoff’s First and Second Circuit Laws were named after the German scientist Gustav Kirchoff, who developed these straightforward guidelines in 1845.

⇒Kirchoff’s First Circuit Law – the law of current:

• “At a circuit junction, the sum of the currents flowing into the junction equals the sum of the currents flowing out of the junction”.

  
  Figure 1 A circuit junction

• Figure 1 shows a circuit junction with two currents ([math] I_1 \; \text{and} \; I_2 [/math]) flowing into the junction and three currents flowing out of the junction ([math] I_3, \; I_4, \; \text{and} \; I_5 [/math]).Kirchoff’s First Circuit Law states:
• [math] I_1 + I_2 = I_3 + I_4 + I_5 [/math]
• Kirchoff’s First Circuit Law is demonstrated in an actual circuit using ammeters in Figure 2
• Since conventional current flows from positive to negative, ammeter [math] A_1 [/math] measures the current entering the junction shown on the diagram.
  At a junction, current divides or recombines, therefore [math] A_2 [/math] and [math] A_3 [/math] measure the current leaving the junction. According to Kirchoff’s First Circuit Law, you can:
• [math] A_1 = A_2 + A_3 [/math]
• Written more generally in mathematical notation the law can be summarized by:
• [math] \sum I_{\text{out  of  junction}} = \sum I_{\text{out  of  junction}} [/math]
• or, in other words, current is conserved at junctions.
• 
  Figure 2 Circuit diagram showing Kirchoff’s First Circuit Law.
• Looked at from a slightly different perspective, as current is the rate of flow of charge, or
• [math] I = \frac{\Delta Q}{\Delta t}[/math]
• “At a circuit junction, the sum of the charge flowing into the junction equals the sum of the charge flowing out of the junction (per second)”.
• [math] \sum Q_{\text{into junction}} = \sum Q_{\text{out of junction}} [/math]

⇒ Kirchoff’s Second Circuit Law – the law of voltages:

• “In a closed-circuit loop, the sum of the potential differences is equal to the sum of the electromotive forces”.
• Figure 3 shows a single closed loop series circuit. In this case, there is one emf and two pds, and Kirchoff’s Second Circuit Law says that:
• 
  Figure 3 Circuit diagram showing Kirchoff’s Second Circuit Law.
• [math] \varepsilon = V_1 + V_2 [/math]
• Or more generally, using mathematical notation, for any closed-circuit loop:
• [math] \sum \varepsilon = \sum V [/math]
• If the circuit is extended to make it a parallel circuit such as Figure 4:
• This parallel circuit is effectively made up of two series circuits: ABCD and AEFD, so:
• [math] \varepsilon = V_1 + V_2 [/math]
• and
• [math] \varepsilon = V_3 + V_4 [/math]
• 
  Figure 4 Circuit diagram showing Kirchoff’s Second Circuit Law in a parallel circuit
• Or
• [math] V_1 + V_2 =V_3 + V_4[/math]
• Kirchoff’s Second Circuit Law holds true for all circuits; but, when it comes to parallel circuits, the circuit has to be seen as a collection of separate series circuits sharing a single power source.
• This equation is founded on the principle of energy conservation: when the charge moves through the circuit components, the energy per coulomb that the battery provided to it, or ε, is converted by the charge into different types of energy.

⇒ Batteries and cells:

• Batteries and cells are essential components in electronics, providing power to devices and systems.
  •  Cells:
    – A cell is a single unit that converts chemical energy into electrical energy.
    – It consists of two electrodes (an anode and a cathode) and an electrolyte.
    – Cells can be primary (non-rechargeable) or secondary (rechargeable).
  • Batteries:
    – A battery is a collection of cells connected together to provide a higher voltage and/or capacity.
  • Batteries can be classified as:
    – Primary (non-rechargeable): used once and then discarded (e.g., alkaline batteries).
    – Secondary (rechargeable): can be recharged and used multiple times (e.g., lead-acid, lithium-ion).
  • Key characteristics:
    – Capacity (C): Measured in ampere-hours (Ah) or milliampere-hours (mAh).
    – Voltage (V): Measured in volts (V).
    – Energy density: Measured in watt-hours per kilogram (Wh/kg).
    – Self-discharge: The rate at which a battery loses its charge when not in use.
  • Types of batteries:
    – Alkaline: Commonly used in flashlights, toys, and other devices.
    – Lead-acid: Used in cars, trucks, and backup power systems.
    – Lithium-ion: Used in portable electronics, electric vehicles, and renewable energy systems.
    – Nickel-cadmium (NiCd): Used in power tools, two-way radios, and other applications.
    – Nickel-metal hydride (NiMH): Used in hybrid and electric vehicles, cordless power tools, and other applications.
  • Battery applications:
    – Portable electronics: Powering devices like smartphones, laptops, and tablets.
    – Electric vehicles: Powering electric cars, buses, and other vehicles.
    – Renewable energy systems: Storing excess energy generated by solar panels and wind turbines.
    – Backup power systems: Providing emergency power during outages and grid failures.

3. Internal resistance and electromotive force:

• Electromotive Force (EMF):
  – EMF is the voltage generated by a cell or battery when no current is flowing through it.
  – Measured in volts (V), it’s the “open-circuit voltage” of a cell or battery.
  – EMF is the maximum voltage a cell or battery can provide.
  
• Internal Resistance:
  – Internal resistance is the opposition to current flow within a cell or battery.
  – Measured in ohms (Ω), it depends on the cell’s or battery’s chemistry, age, and other factors.
  – Internal resistance causes a voltage drop when current flows, reducing the available voltage.
• Relationship between EMF and Internal Resistance:
  – When current flows, the internal resistance reduces the voltage available from the EMF.
  – The higher the internal resistance, the greater the voltage drop.
  – The lower the internal resistance, the closer the available voltage is to the EMF.
• Internal resistance, or r, is a constant feature of real power sources, such batteries and lab power packs.
• The power supply’s internal resistance produces a potential difference as current passes through it, which causes electrical energy to be converted to heat energy.
• This is one of the causes of the warming up of portable electronics like tablets after extended usage.
• Since internal resistance is located “inside” a power source, it cannot be tested directly.
• It can only be measured by applying its electrical characteristic.
• Figure 5 illustrates a circuit that may be used to do this.
• 
  Figure 5 A circuit used to measure the internal resistance and electromotive force of a real power supply and a real power supply
• According to Kirchoff’s Second Circuit Law, the electromotive force, ε, must equal the total of the potential differences in the circuit.
• In this circuit, there are two potential differences: the pd across the internal resistor and the one across the external variable resistor (V).
• The pd across this resistor is equal to Ir, however this cannot be determined precisely.
  This implies that:
• [math]\varepsilon = V + Ir[/math]
• The current, I, can be measured directly using an ammeter; ε and r are both constants, so the equation can be rewritten as:
• [math]V = \varepsilon – Ir[/math]
• Or
• [math]V = -rI + \varepsilon [/math]
• It is the equation for a straight line with a negative gradient that looks like this: y = mx + c.
• The electromotive force, ε, is the graph’s y-intercept, and the gradient is negative and equal to –r, the internal resistance, if an electrical characteristic is created using values of V and I from different values of R (the external load resistance).

⇒ Voltmeters and ammeters:

• Voltmeters and ammeters are essential instruments in electronics for measuring voltage and current, respectively.
• Voltmeters:
  – Measure the voltage between two points in a circuit.
  – Typically connected in parallel with the component or circuit being measured.
• Types:
  – Analog voltmeters (pointer-type)
  – Digital voltmeters (display numerical values)
  – Units: Volts (V)
• Ammeters:
  – Measure the current flowing through a circuit or component.
  – Typically connected in series with the component or circuit being measured.
• Types:
  – Analog ammeters (pointer-type)
  – Digital ammeters (display numerical values)
• Units: Amperes (A)
• Differences:
  – Voltmeters measure voltage (potential difference) between two points.
  – Ammeters measure current (flow of electrons) through a circuit or component.
  – Voltmeters are connected in parallel, while ammeters are connected in series.
• Important considerations:
  – When using a voltmeter, ensure it connected correctly to avoid damaging the meter or the circuit.
  – When using an ammeter, ensure it’s connected in series and can handle the current being measured to avoid damage or safety risks.
  – Always consult the instrument’s manual for proper usage and safety guidelines.
• 
  Figure 6 Moving coil ammeter.
• The coil turns as a result of the current flowing through it interacting with a permanent magnetic field; the current is then shown by a pointer on an analogue scale.
• Modern digital ammeters measure current using an integrated circuit inside the meter, and then show the result on a numerical display.
• Nonetheless, because every component inserted into the circuit in series has resistance, both designs will always have an impact on the current’s magnitude.
• Therefore, the ammeter’s additional resistance will lower the circuit’s current.
• Modern ammeters are made to have extremely low resistances and are calibrated to account for the drop in current caused by the meter’s resistance since this effect cannot be overcome.
• 
  Figure 7 Ammeters have low resistance, and voltmeters have high resistance.
• Voltmeters are generally linked in parallel with other components in circuits.
• The operation of analogue and digital voltmeters is essentially similar to that of ammeters.
• However, in order to make the current proportionate to the potential difference, a tiny current is taken from the circuit and flows through a known, fixed extremely high resistance resistor.
• As a result, premium voltmeters have extremely high resistance.

4. Resistor networks:

• Every component provides a specific amount of resistance to the circuit when it is joined to other components to create functional circuits.
• Whether a component is linked in series or parallel with other components determines how the additional resistance affects the circuit.
• The total resistance of components linked in parallel or series may be determined using a few straightforward formulas.

⇒ Resistors connected in series:

• Consider the resistor network shown in Figure 8 and 9.

  
  Figure 8 Circuit diagram showing
  resistor combinations in series.
  
  Figure 9 Circuit diagram showing
  equivalent resistor

• Figure 9 represents the single resistor that could replace the three resistors in series in Figure 8.
• Using Kirchoff’s Circuit laws and Ohm’s law leads to:
• [math] \varepsilon = V_1 + V_2 + V_3 [/math]
• and
• [math] \varepsilon =V_T [/math]
• where
• [math] V_T = V_1 + V_2 + V_3  \qquad [/math]
• So,
• [math] V = IR [/math]
• Put in equation according to resistor and volt then
• [math] IR_T = IR_1 + IR_2 + IR_3 \\ IR_T = I(R_1 + R_2 + R_3) [/math]
• So,
• [math] R_T = R_1 + R_2 + R_3 [/math]
• and for a series network of n resistors:
• [math] R_T = R_1 + R_2 + R_3 + \dots + R_n [/math]
• or, using sigma notation
• [math] R_T = \sum_{i=1}^{n} R_i [/math]

⇒ Resistors connected in parallel:

• Consider the following circuit:
• 
  Figure 10 Circuit diagram showing resistors connected in parallel
• In the right-hand circuit one resistor, RT, has been used to replace all three resistors arranged in parallel in the left-hand circuit.
• Again, using Kirchoff’s Circuit laws and Again, using Kirchoff’s Circuit laws and the definition of resistance,
• [math] V = IR [/math]
• Kirchoff’s First Circuit law says:
• [math] I_T = I_1 + I_2 + I_3 [/math]
• And
• [math] I = \frac{V}{R} [/math]
• So as the potential difference, , is the same across all of the resistors:
• [math] I_T = \frac{V_T}{R_1} + \frac{V_T}{R_2} + \frac{V_T}{R_3} \\ I_T = V_T \left( \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \right) [/math]
• Rearranging
• [math] \frac{I_T}{V_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \\ \frac{I_T}{V_T} = \frac{1}{R_T} [/math]
• So,
• [math] \frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} [/math]
• For a network of n resistors connected in parallel
• [math]  \frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots + \frac{1}{R_n} [/math]
• or using sigma notation:
• [math]  \frac{1}{R_T} = \sum_{i=1}^{n} \frac{1}{R_i}[/math]
• To summarize, the total resistance of a series of resistors is equal to the sum of its individual resistances.
• The reciprocal of the total resistance for resistors connected in parallel is equal to the reciprocal of each individual resistance.
• The resistance of a parallel arrangement of resistors is always smaller than the resistance of any individual resistor in that combination.

5. Potential dividers:

• A fundamental concept in electronics, used to reduce a voltage level or divide a voltage ratio.
• A potential divider is a resistor network that divides an input voltage ([math] V_{in} [/math]) into a smaller output voltage ([math] V_{out} [/math]). It consists of two resistors, [math] R_1 \text{ and, } R_2 [/math] connected in series.
• Working:
  1. The input voltage ([math] V_{in} [/math]) is applied across the series combination of [math] R_1 and R_2 [/math].
  2. The voltage across [math]R_2( V_{out}) [/math] is proportional to the ratio of [math] R_2 [/math]to the total resistance [math](R_1 + R_2) [/math].
  3. By adjusting [math]R_1 and R_2 [/math], the output voltage [math](V_{out}) [/math] can be set to a specific value.
• Types:
  1. Fixed Potential Divider: Uses fixed resistors to divide the voltage.
  2. Variable Potential Divider: Uses a potentiometer (variable resistor) to adjust the output voltage.
• The potential divider formula assumes ideal resistors and neglects loading effects.
• In practice, the output voltage may vary due to resistor tolerances and loading.
• 
  Figure 11 Circuit diagram of a potential divider
• Generally, we are trying to vary the potential difference (across ) by varying .
• Assuming that the cell has negligible internal resistance, then the total resistance of the circuit  is given by:
• [math] R_T = R_1 + R_2 [/math]
• by using the Ohm’s law
• [math] I = \frac{V}{R} = \frac{\varepsilon}{R_T} = \frac{\varepsilon}{R_1 + R_2} [/math]
• Then considering the resistor R1 we can write:
• [math] V_1 = IR_1 [/math]
• Substituting:
• [math] V_1 = \frac{\varepsilon}{R_1 + R_2} \cdot R_1[/math]
• [math] V_1 = \frac{\varepsilon R_1}{R_1 + R_2} [/math]
• From this equation it can be seen that if ε and [math] R_1[/math] are fixed, then [math] V_1 [/math] only depends on [math] R_2 [/math]. In fact, as [math] R_2 [/math] increases, [math] V_1 [/math] decreases, and vice versa.

⇒ Potential dividers as sensors:

• Potential dividers can be used as sensors to measure various physical parameters, such as:
  1. Temperature: By using a thermistor or a temperature-dependent resistor in the potential divider circuit, the output voltage can be made to vary with temperature.
  2. Light: A photoresistor or light-dependent resistor can be used to measure light intensity.
  3. Pressure: A pressure-dependent resistor or a piezoresistor can be used to measure pressure changes.
  4. Position: A potentiometer can be used as a position sensor, where the output voltage indicates the position of the wiper.
  5. Force: A force-sensing resistor or a piezoresistor can be used to measure force or weight.
  6. Humidity: A humidity-dependent resistor can be used to measure humidity levels.
  7. pH: A pH-dependent resistor can be used to measure the acidity or basicity of a solution.
• The potential divider sensor circuit typically consists of:
  1. A voltage source [math](V_{in}) [/math]
  2. A sensor resistor [math](R_{sense}) [/math] that changes value with the physical parameter being measured
  3. A fixed resistor [math] (R_{fixed}) [/math]
  4. A voltage output [math](R_{out}) [/math] that varies with the sensor resistance
• By measuring the output voltage [math](R_{out}) [/math], the physical parameter can be inferred. Potential divider sensors are simple, low-cost, and widely used in various applications.
• 
  Figure 12 A thermistor potential divider circuit and the resistance–temperature graph for a ntc thermistor
• [math]R_2 [/math] is replaced by a thermistor coupled to an electronic thermometer.
• Negative temperature coefficient, or NTC, thermistors make up the majority of thermistors.
• This indicates that, as the temperature rises, their resistance falls, as seen in Figure 12, which also includes a circuit schematic illustrating the connections between the parts:
• As the temperature rises, the resistance of the thermistor,[math] R_2 [/math] , decreases and [math]V_1 [/math] increases, which has an impact on the potential difference across the fixed resistor [math]R_1 [/math] in figure 11.
• As a result, rising temperatures lead to rising pd. Conversely, if the voltmeter is connected across the thermistor, a rise in temperature will result in a fall in pd.
• The voltmeter is often connected across the fixed resistor since most applications call for the pd to rise with temperature.
• Using a light-dependent resistor yields a comparable result (LDR).
• These parts serve as excellent light sensors since they alter in resistance in response to changes in light intensity.
• Since semi-conducting materials are used to make LDRs, light may flow through them and release electrons from their structural bonds, lowering the LDR’s resistance.
• LDRs can have resistances as high as megaohms while operating in the dark, but they can also have resistances as low as a few hundred ohms when operating in the light.
• When an LDR is used in place of [math] R_2 [/math] in a potential divider circuit, the output voltage  across the fixed resistor will grow in tandem with the intensity of the light.
• 
  Figure 13 An LDR: its electrical circuit symbol (a) resistance– light intensity graph (b) and its use in a potential divider circuit (c).