Lesson 5.4: EMF, Internal Resistance and Potential Dividers
Introduction
Welcome to Lesson 5.4 of Foundation Physics! In this lesson, students, we’re going to dive deep into the fascinating world of electricity, focusing on electromotive force (e.m.f.), internal resistance, and potential dividers. Our key objectives today are to:
- Understand what real cells are, including their e.m.f., internal resistance, and terminal potential difference (p.d.).
- Measure internal resistance graphically.
- Explore the potential divider and how it provides a variable output.
- Investigate sensor circuits that use thermistors and light-dependent resistors.
- Calculate terminal p.d. and see the effects of internal resistance.
Let’s get started! ⚡
Understanding Electromotive Force (e.m.f.)
When we talk about e.m.f., we are referring to the energy provided by a cell or battery per unit charge. It is what pushes electrons through a circuit. The formula for e.m.f. can be expressed as:
$$
$E = \frac{W}{Q}$
$$
where:
- $E$ is the e.m.f.
- $W$ is the work done (in joules)
- $Q$ is the charge (in coulombs)
A good analogy for e.m.f. is imagining a water pump. Just as a pump pushes water through pipes, the e.m.f. pushes charged particles through a circuit.
Real Cells
Real cells aren't perfect; they have internal resistance. This is the resistance within the cell itself that affects the current output. When a cell provides current to a circuit, there is a voltage drop across this internal resistance, which can be described by:
$$
$V = I(R + r)$
$$
where:
- $V$ is the terminal voltage
- $I$ is the current
- $R$ is the resistance of the external circuit
- $r$ is the internal resistance of the cell
Therefore, the actual voltage you get at the terminals of the cell (the terminal p.d.) is less than the e.m.f. due to this internal resistance.
Measuring Internal Resistance Graphically
One way to find the internal resistance of a cell is by using a graphical method. We can set up a circuit to measure current and terminal voltage. By using ohm's law, we can plot a graph of voltage ($V$) against current ($I$). The internal resistance $r$ can be extracted from the slope of this line:
- The y-intercept gives the e.m.f.
- The slope gives $-r$.
If we have a graph with the line equation in the form:
$$
$V = E - Ir$
$$
This shows the relationship where the more current we draw, the lower the voltage, indicating internal resistance. 🎉
Exploring Potential Dividers
Another crucial concept in electric circuits is the potential divider, which is a simple circuit that can provide a variable output voltage. It consists of two resistors, $R_1$ and $R_2$, in series across a voltage supply, and we can calculate the output voltage ($V_{out}$) across one of the resistors:
$$
V_{out} = $\frac{R_2}{R_1 + R_2}$ $\times$ V_{in}
$$
where:
- $V_{in}$ is the total input voltage across the series resistors.
The beauty of a potential divider is that it creates a variable voltage output depending on the ratio of the resistances. For example, if $R_1 = 1kΩ$ and $R_2 = 3kΩ$, and our supply voltage ($V_{in}$) is 12V, we can find $V_{out}$ as follows:
$$
V_{out} = $\frac{3kΩ}{1kΩ + 3kΩ}$ $\times 12$V = 9V$$
This principle is vital in applications like adjusting volume on speakers or changing brightness in lighting systems. ✨
Sensor Circuits Using Thermistors and Light-Dependent Resistors
Sensor circuits often utilize components such as thermistors (temperature-dependent resistors) and light-dependent resistors (LDRs) to detect changes in temperature and light, respectively. These components can act as part of a potential divider.
For example, consider a thermistor in a potential divider with a fixed resistor. The output voltage changes based on the temperature, allowing us to use this circuit for temperature sensing. The relationship can be modeled similarly:
$$
V_{out} = $\frac{R_{th}}{R + R_{th}}$ $\times$ V_{in}
$$
where $R_{th}$ is the resistance of the thermistor which varies with temperature.
Using these circuits in real-world applications could mean switching a fan on when a room gets too hot, demonstrating the power of these solid-state devices! 🌡️
Conclusion
In this lesson, students, we've explored the principles of e.m.f. and internal resistance in real cells, learned how to measure internal resistance graphically, and examined the workings of potential dividers and sensor circuits. These concepts form the basis for understanding how electric circuits function in our daily lives, from powering your phone to controlling the temperature at home.
Study Notes
- Electromotive Force (e.m.f.) is the energy per charge provided by a source.
- Internal resistance reduces terminal p.d., calculated as $V = I(R + r)$.
- Measure internal resistance graphically using the slope of a $V-I$ graph.
- A potential divider varies output voltage based on resistor ratios: $V_{out} = \frac{R_2}{R_1 + R_2} \times V_{in}$.
- Sensor circuits can use thermistors and LDRs to provide variable output based on environmental changes.