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Ohm's Law and Resistive Circuits
Ohm’s law is the cornerstone of basic electrical engineering and physics. It describes the linear relationship between the voltage across a conductor, the current flowing through it, and its…
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During an experiment, the measured U/I ratio remains constant at 100 Ω. What does this constant value represent?
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A lamp is powered with a current of 2 A and a voltage of 24 V. What is its resistance?
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Given the tabulated measurements U (V): 1.5, 3.0, 4.5 … and I (A): 0.015, 0.030, 0.045 …, which type of curve best fits the plotted graph of U versus I?
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From the same data set, the coefficient of proportionality (slope) of the U‑I graph is calculated. What is its value?
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If a dipole shows a linear U‑I characteristic but the measured slope is 80 Ω, what conclusion follows regarding its ohmic nature?
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When using an ohmmeter to measure a resistor, which of the following statements is true?
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In the experimental setup, why does increasing the generator voltage lead to a proportional increase in current through the 100 Ω resistor?
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If a resistor is described as a "dipôle non polarisé", which of the following is implied?
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When plotting the characteristic of a resistor using the scales 1 cm → 2 V and 1 cm → 20 mA, what is the physical meaning of the slope of the resulting line?
Understanding Ohm’s Law and Resistive Circuits
Ohm’s law is the cornerstone of basic electrical engineering and physics. It describes the linear relationship between the voltage across a conductor, the current flowing through it, and its resistance. This course will walk you through the fundamental concepts, illustrate them with practical examples, and explain how to interpret experimental data. By the end, you will be able to solve typical problems involving resistors, analyze U‑I (voltage‑current) graphs, and understand how measurement devices such as ohmmeters work.
1. The Core Statement of Ohm’s Law
Ohm’s law can be written in three equivalent forms:
- V = I·R – voltage equals current multiplied by resistance.
- I = V/R – current equals voltage divided by resistance.
- R = V/I – resistance is the ratio of voltage to current.
These relationships hold for an ohmic component, meaning the resistance remains constant over the range of applied voltages and currents. For a 100 Ω resistor, the correct description of the voltage‑current relationship is:
- The voltage equals the current multiplied by 100 Ω.
This directly follows from the first form of Ohm’s law.
2. Interpreting a Constant U/I Ratio
When you measure voltage (U) and current (I) for a resistor and find that the ratio U/I stays constant at 100 Ω, you have identified the resistor’s resistance. The constant ratio is not a measure of power, voltage drop, or conductance; it is the definition of resistance:
- Resistance (R) = U/I = 100 Ω
Because the ratio does not change with varying voltage, the component behaves ohmically.
3. Calculating Resistance from Real‑World Data
Consider a lamp that draws a current of 2 A while a voltage of 24 V is applied. Using Ohm’s law:
R = V / I = 24 V / 2 A = 12 Ω
Thus the lamp’s effective resistance under those operating conditions is 12 Ω. This example shows how Ohm’s law can be applied even to devices that are not perfectly linear; the calculated resistance represents the average value at the given operating point.
4. Recognizing the Shape of a U‑I Graph
When you plot voltage (U) on the vertical axis and current (I) on the horizontal axis for an ohmic resistor, the points lie on a straight line passing through the origin**. This linear relationship arises because:
- U = I·R → U/I = R (a constant).
- When I = 0, U must also be 0, giving the origin.
Any deviation from a straight line (e.g., a curve that bends upward or downward) indicates a non‑ohmic behavior, such as that of a diode or a filament lamp whose resistance changes with temperature.
5. Determining the Slope (Coefficient of Proportionality)
The slope of the U‑I line is the resistance value. Using the data set:
- U = 1.5 V, I = 0.015 A → R = 1.5 / 0.015 = 100 Ω
- U = 3.0 V, I = 0.030 A → R = 3.0 / 0.030 = 100 Ω
All points give the same ratio, confirming a slope of 100 Ω. This constant slope is the hallmark of an ohmic component.
6. Assessing Ohmic Behavior When the Slope Differs
If a dipole (two‑terminal device) shows a linear U‑I characteristic with a measured slope of 80 Ω, the component is still ohmic. Ohmic behavior does not require a specific resistance value; it only requires that the resistance remain constant over the measured range. Therefore, the correct conclusion is:
- It is an ohmic dipole with resistance 80 Ω.
The value of 80 Ω simply tells you the magnitude of the resistance, not whether the device obeys Ohm’s law.
7. How an Ohmmeter Measures Resistance
Modern digital ohmmeters determine resistance by applying a known small voltage across the terminals and measuring the resulting current. The device then computes R = V/I internally. This method is accurate because it directly uses Ohm’s law. The other listed statements—measuring temperature change, counting electron flow, or detecting magnetic fields—are not how standard ohmmeters operate.
8. Why Increasing Generator Voltage Increases Current Proportionally
When a variable voltage source is connected to a 100 Ω resistor, the current follows the rule I = V / R. As the generator voltage rises, the current rises in direct proportion because the resistance stays fixed. This linear relationship is a practical illustration of Ohm’s law in action:
- Doubling the voltage doubles the current.
- Tripling the voltage triples the current, and so on.
The statement that “the resistor obeys Ohm's law, linking voltage and current linearly” captures the underlying physics.
9. Practical Tips for Working with Ohmic Components
- Always verify linearity. Plot U versus I; a straight line through the origin confirms ohmic behavior.
- Check temperature effects. Some resistors change resistance with temperature; keep the component within its rated range for accurate measurements.
- Use proper measurement tools. An ohmmeter applies a safe test voltage; never use a high‑current source to infer resistance directly.
- Remember power limits. Power dissipated is P = V·I = I²·R = V²/R. Exceeding the rated power can damage the resistor and alter its resistance.
10. Summary of Key Concepts
To master Ohm’s law and resistive circuits, remember the following points:
- Ohm’s law links voltage, current, and resistance with the simple equation V = I·R.
- A constant U/I ratio represents the resistance of an ohmic component.
- Linear U‑I graphs that pass through the origin indicate a constant resistance.
- The slope of the U‑I line is the resistance value.
- Ohmic behavior is defined by a constant resistance, not by a specific numeric value.
- Ohmmeters determine resistance by applying a known voltage and measuring the resulting current.
- Increasing source voltage across a fixed resistor leads to a proportional increase in current, illustrating Ohm’s law in practice.
11. Frequently Asked Questions (FAQ)
Is every resistor automatically ohmic?
Most standard resistors are designed to be ohmic over a wide range of voltages and currents. However, extreme temperatures or high power levels can cause their resistance to change, making them temporarily non‑ohmic.
Can a device be linear but non‑ohmic?
Linearity alone does not guarantee ohmic behavior; the line must also pass through the origin. A linear graph that intercepts the voltage axis at a non‑zero value indicates a fixed offset (e.g., a battery with internal resistance), which is not purely ohmic.
Why do filament lamps appear non‑ohmic?
When a filament lamp heats up, its resistance increases dramatically, causing the U‑I curve to bend upward. This temperature‑dependent change makes the lamp non‑ohmic under normal operating conditions.
12. Applying the Knowledge: Sample Problem
Problem: A circuit contains a 100 Ω resistor and a variable voltage source. If the source is set to 15 V, what current flows through the resistor? If the voltage is increased to 30 V, what is the new current?
Solution: Using I = V / R:
- For V = 15 V: I = 15 V / 100 Ω = 0.15 A.
- For V = 30 V: I = 30 V / 100 Ω = 0.30 A.
The current doubles when the voltage doubles, confirming the linear relationship predicted by Ohm’s law.
13. Further Reading and Resources
- Wikipedia – Ohm’s Law
- All About Circuits – Ohm’s Law Tutorial
- Electronics Tutorials – DC Circuits
By mastering these concepts, you will be equipped to analyze and design basic electrical circuits, interpret experimental data accurately, and troubleshoot real‑world electronic devices.
