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.
Electromotive force
The electromotive force (emf) is the work done per unit charge to move a charge completely around a circuit, including through the battery.
- However, this is rarely the case.
- Inside every battery, there is a hidden obstacle: internal resistance.
The emf is the maximum potential difference the battery can provide when no current is flowing.
What is Internal Resistance?
Internal resistance
Internal resistance is the resistance within the battery itself, caused by the materials and chemical reactions inside it.
This resistance reduces the energy available to the external circuit.
How Does Internal Resistance Affect a Circuit?
- When a current $I$ flows through a battery with emf $\varepsilon$ and internal resistance $r$, the potential difference across the battery’s terminals (the terminal voltage) is less than the emf.
- This is because some energy is lost as heat within the battery.
- The relationship is given by: $$V = \varepsilon - Ir$$ where:
- $V$ is the terminal voltage.
- $I$ is the current flowing through the circuit.
- $r$ is the internal resistance.
- If a battery has an emf of 12 V and an internal resistance of 0.5 Ω, and it supplies a current of 2 A to a circuit, the terminal voltage is: $$V = 12 \, \text{V} - (2 \, \text{A} \times 0.5 \, \Omega) = 11 \, \text{V}$$
- This means 1 V is lost inside the battery due to its internal resistance.
Calculating Internal Resistance
- The total resistance in a circuit with a battery is the sum of the internal resistance $r$ and the external resistance $R$.
- Using Ohm’s Law, the current $I$ in the circuit is:
$$I = \frac{\varepsilon}{R + r}$$
Example- A battery with an emf of 9 V and an internal resistance of 1 Ω is connected to a 4 Ω resistor.
- The current in the circuit is: $$I = \frac{9 \, \text{V}}{4 \, \Omega + 1 \, \Omega} = 1.8 \, \text{A}$$
- The terminal voltage is: $$V = 9 \, \text{V} - (1.8 \, \text{A} \times 1 \, \Omega) = 7.2 \, \text{V}$$
To find the internal resistance of a battery, measure the terminal voltage at two different currents. The difference in voltage divided by the difference in current givesr.
Variable Resistors: Controlling Current and Voltage
Variable resistors
Variable resistors are components that allow you to adjust the resistance in a circuit.
They are essential for controlling current and voltage in various applications.
Let’s explore three common types: thermistors, light-dependent resistors (LDRs), and potentiometers.
Thermistors
Thermistor
A thermistor is a resistor whose resistance changes with temperature.
