Physics (9702) | Practical circuits

Welcome to Practical Circuits!

Hey there, future electrician! This chapter takes everything you learned about current, voltage, and resistance and puts it into action. Understanding practical circuits is crucial—it's how we design everything from simple flashlights to complex electronic sensors.
We will explore the crucial difference between a battery's total energy supply (e.m.f.) and the energy available to the components (p.d.), and master the powerful tools known as Kirchhoff's Laws. By the end, you'll be able to analyze almost any DC circuit!

10.1 Practical Circuit Fundamentals

10.1.1 Circuit Diagrams and Symbols

Before solving problems, we must be fluent in the language of circuits. You need to be able to recall and use the standard circuit symbols and draw and interpret circuit diagrams correctly.

Think of circuit symbols like letters in a sentence. If you mix them up, the meaning is lost!

10.1.2 Electromotive Force (e.m.f.)

The electromotive force (e.m.f.) is the fundamental energy supplier in a circuit, usually provided by a cell or power source.

Definition: The e.m.f. (\(E\)) of a source is the energy transferred per unit charge in driving charge around a complete circuit.

It represents the total electrical energy that the source converts from other forms (chemical, mechanical) and makes available to the charge carriers.

The unit for e.m.f. is the volt (V), which is Joules per Coulomb (J C\(^{-1}\)).

10.1.3 Potential Difference (p.d.) vs. E.M.F.

This is a common source of confusion, but the distinction is vital and relates to energy considerations.

Potential Difference (p.d.): This is the energy transferred (or converted) per unit charge when charge passes between two points in a circuit (usually across a component like a resistor).

Analogy: The Water Pump and the Waterfall

• The E.M.F. (\(E\)) is like the total energy supplied by the water pump to lift the water to the top of the system. It represents the total potential energy input.
• The P.D. (\(V\)) across a resistor is like the energy released when the water drops down a waterfall (the resistor). It represents the energy converted/dissipated as it flows through the component.

Key Takeaway:
In a perfect circuit with no internal losses: \(E\) (supplied) = \(\Sigma V\) (dropped across components).

10.1.4 The Effect of Internal Resistance

In reality, all power sources (batteries, generators) have some resistance within them. This is called internal resistance (\(r\)).

When the battery is connected to a circuit, some of the energy supplied (e.m.f.) is wasted overcoming this internal resistance, causing the battery itself to heat up.

The p.d. actually delivered to the external circuit is called the terminal potential difference (\(V_t\)).

The total e.m.f. (\(E\)) is split into two parts:
1. The useful p.d. delivered to the external circuit, \(V_t\).
2. The lost volts, \(Ir\), dissipated internally.

Terminal P.D. Equation:
\[E = V_t + Ir\]
Since \(V_t = IR\), where \(R\) is the total external resistance, we can also write:
\[E = IR + Ir = I(R + r)\]

Impact on Terminal P.D.:
When a high current (\(I\)) is drawn, the 'lost volts' (\(Ir\)) increase, causing the terminal p.d. (\(V_t = E - Ir\)) to decrease.
Example: If you start your car (which draws a very high current), the headlights momentarily dim because the high current causes a significant drop in the terminal p.d. of the battery due to its internal resistance.

10.2 Kirchhoff's Laws: The Rules of Current Flow

Kirchhoff's laws are essential for analyzing complex circuits, especially those that cannot be simplified by simple series/parallel combinations.

10.2.1 Kirchhoff's First Law (KCL)

This law deals with current and points (junctions) in a circuit.

Statement: The sum of the currents entering any junction in a circuit is equal to the sum of the currents leaving that junction.

Underlying Principle: Conservation of Charge
Since charge cannot be created or destroyed, it must be conserved. Whatever amount of charge flows into a point must flow out.

In simple terms: What goes in, must come out.
\[\Sigma I_{in} = \Sigma I_{out}\]

Example: If a main wire carrying 5 A splits into two branches, one branch carries 2 A, the other must carry 3 A.

10.2.2 Kirchhoff's Second Law (KVL)

This law deals with voltage and paths (loops) in a circuit.

Statement: For any closed loop in a circuit, the sum of the e.m.f.s is equal to the sum of the potential differences (p.d.s) around the loop.

Underlying Principle: Conservation of Energy
If you travel around a closed circuit loop, you end up back where you started. Therefore, the total energy supplied by the sources (e.m.f.s) must equal the total energy dissipated by the components (p.d.s).

In simple terms: Total voltage gained = Total voltage dropped.
\[\Sigma E = \Sigma V\]

Memory Aid:
K1L: Current, Charge, Junctions.
K2L: Voltage, Energy, Loops.

10.2.3 Resistance in Series and Parallel (Derived from Kirchhoff's Laws)

Resistors in Series

When resistors are connected in series, there is only one path for the current (\(I\)).
Applying K2L to the loop: \(E = V_1 + V_2 + ...\)
Using Ohm's Law (\(V = IR\)): \(IR_{total} = IR_1 + IR_2 + ...\)
Since \(I\) is constant, we divide by \(I\):

Series Resistance Formula:
\[R_{total} = R_1 + R_2 + R_3 + ...\]

Key Takeaway: Resistance increases when resistors are added in series.

Resistors in Parallel

When resistors are connected in parallel, the voltage (\(V\)) across each resistor is the same, but the current splits (K1L).
Applying K1L at the junction: \(I_{total} = I_1 + I_2 + I_3 + ...\)
Using Ohm's Law rearranged (\(I = V/R\)): \(V/R_{total} = V/R_1 + V/R_2 + ...\)
Since \(V\) is constant, we divide by \(V\):

Parallel Resistance Formula:
\[\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ...\]

Key Takeaway: Resistance decreases when resistors are added in parallel. The total resistance is always less than the smallest individual resistance.

10.3 Potential Dividers

Many real-world circuits require a voltage output that is only a fraction of the supply voltage. A potential divider (or voltage divider) does exactly this—it splits the supply p.d. into smaller proportions.

10.3.1 The Principle of the Potential Divider

A potential divider consists of two or more resistors connected in series across a supply voltage (\(V_{in}\)). Since they are in series, the supply voltage is divided across the resistors proportionally to their resistances.

Consider two resistors, \(R_1\) and \(R_2\), in series with supply voltage \(V_{in}\). The output voltage (\(V_{out}\)) is taken across \(R_2\).

The current in the circuit is \(I = V_{in} / (R_1 + R_2)\).

The output voltage (\(V_{out}\)) across \(R_2\) is \(V_{out} = IR_2\).

Substituting the expression for \(I\) gives the Potential Divider Formula:
\[V_{out} = V_{in} \left( \frac{R_2}{R_1 + R_2} \right)\]

This formula shows that \(V_{out}\) is simply the fraction of the total resistance (\(R_2 / R_{total}\)) multiplied by the total input voltage (\(V_{in}\)).

10.3.2 The Potentiometer and Null Methods

A potentiometer is essentially a variable potential divider. It typically uses a long wire or resistive track where a sliding contact allows the output voltage to be tapped at any point, providing a smoothly variable output p.d. from zero up to the full supply e.m.f.

Use in Comparing Potential Differences:
Potentiometers are historically used to accurately compare the e.m.f.s of two cells or sources by using a null method.

A null method involves adjusting the output of the potentiometer until a galvanometer connected in the circuit reads exactly zero current (a 'null' reading).

Why use a null method?
When the current is zero, the measuring circuit draws no current from the cell being tested. This means there are no lost volts (\(Ir\)), and the measured terminal p.d. is exactly equal to the cell's true e.m.f. (\(E\)). This provides the most accurate measurement.

10.3.3 Sensor Circuits: Thermistors and LDRs

Potential dividers are crucial for building sensor circuits. By replacing one of the fixed resistors (\(R_1\) or \(R_2\)) with a variable resistance sensor (like an LDR or thermistor), we create a circuit whose output voltage (\(V_{out}\)) is dependent on an external physical condition (light or temperature).

Using a Light-Dependent Resistor (LDR)

An LDR's resistance decreases as light intensity increases.

Application: Automatic Lighting
If the LDR is used as \(R_2\) in the potential divider formula:

• When it is dark, LDR resistance is high. \(V_{out}\) (across the LDR) is high. This high voltage can trigger a circuit (like a street light switch) to turn on.
• When it is bright, LDR resistance is low. \(V_{out}\) is low. The circuit remains off.

Using a Thermistor (NTC type)

A standard thermistor (NTC – Negative Temperature Coefficient) has a resistance that decreases as temperature increases.

Application: Temperature Control (e.g., car dashboard warning)
If the Thermistor is used as \(R_2\) in the potential divider formula:

• When the temperature is low (e.g., engine cold), Thermistor resistance is high. \(V_{out}\) (across the thermistor) is high.
• When the temperature is high (e.g., engine overheating), Thermistor resistance is low. \(V_{out}\) is low. This low voltage can trigger an alarm or fan.