B.5.5 Electric Cells and Variable Resistors

Internal Resistance and Variable Resistors

Internal Resistance: Understanding the Real-World Limitations of Electric Cells

• When you connect a battery to a circuit, you might expect it to deliver its full electromotive force (emf) to the external components.

• However, this is rarely the case.
• Inside every battery, there is a hidden obstacle: internal resistance.

What is Internal Resistance?

How Does Internal Resistance Affect a Circuit?

1. When a current $I$ flows through a battery with emf $\epsilon$ and internal resistance $r$, the potential difference across the battery’s terminals (the terminal voltage) is less than the emf.
2. This is because some energy is lost as heat within the battery.
3. The relationship is given by:

$$V=\epsilon -Ir$$

where:

• $V$ is the terminal voltage.
• $I$ is the current flowing through the circuit.
• $r$ is the internal resistance.

Calculating Internal Resistance

1. The total resistance in a circuit with a battery is the sum of the internal resistance $r$ and the external resistance $R$.
2. Using Ohm’s Law, the current $I$ in the circuit is:

$$I=\frac{\epsilon }{R+r}$$

Variable Resistors: Controlling Current and Voltage

Let’s explore three common types: thermistors, light-dependent resistors (LDRs), and potentiometers.

Thermistors

There are two main types:

• NTC (Negative Temperature Coefficient) Thermistors: Resistance decreases as temperature increases.
• PTC (Positive Temperature Coefficient) Thermistors: Resistance increases as temperature increases.

Light-Dependent Resistors (LDRs)

Potentiometers

• By moving the slider, you can change the resistance between the terminals, allowing you to control the voltage output.

Internal Resistance and Variable Resistors in Circuits

Internal Resistance in Circuit Analysis

When analyzing circuits with internal resistance:

1. Identify the emf $\epsilon$ and internal resistance $r$ of the battery.
2. Calculate the total resistance $R+r$ in the circuit.
3. Use Ohm’s Law to find the current: $I=\frac{\epsilon }{R+r}$
4. Determine the terminal voltage: $V=\epsilon -Ir$

Practical Considerations and Challenges

Internal Resistance

• Energy Loss: Internal resistance causes energy to be lost as heat, reducing the efficiency of the battery.
• Voltage Drop: As current increases, the voltage drop across the internal resistance increases, further reducing the terminal voltage.

Variable Resistors

• Non-Linear Behaviour: Thermistors and LDRs often exhibit non-linear resistance changes, which can complicate circuit design.
• Wear and Tear: Potentiometers can wear out over time due to mechanical movement.

Reflection and Broader Implications