Question

What are meant by ohmic and non-ohmic resistances? Draw the graph between voltage and current for a non-ohmic circuit and define dynamic resistance.

Hint:

Ohmic resistors obey Ohm's Law, and their resistance is constant regardless of the voltage or current. Non-ohmic resistors, however, exhibit a variable resistance that depends on factors like voltage and temperature. Dynamic resistance measures the instantaneous resistance of non-ohmic materials.

Answer 1

- **Ohmic Resistance:** Ohmic resistance refers to the type of resistance exhibited by materials that follow Ohm's Law, which states that the current passing through a conductor is directly proportional to the voltage applied across it, with the proportionality constant being the resistance. Mathematically, Ohm’s Law is represented as: \[ V = I R \] where \( V \) is the voltage, \( I \) is the current, and \( R \) is the resistance. In ohmic materials, the resistance remains constant regardless of changes in the applied voltage or current. The graph of voltage \( V \) versus current \( I \) for an ohmic material is a straight line, indicating a constant resistance. For example, metals like copper and aluminum are ohmic resistors, as they maintain a linear relationship between voltage and current. The key point is that for ohmic resistors, the resistance does not change with temperature or voltage, as long as the material remains within its linear region. In other words, if we apply a higher voltage to an ohmic material, the current will increase proportionally, and the ratio of voltage to current will stay the same. - **Non-Ohmic Resistance:** Non-ohmic resistance refers to the resistance shown by materials that do not obey Ohm’s Law. In these materials, the relationship between the voltage and the current is not linear, and the resistance changes with varying voltage or current. Non-ohmic materials exhibit a variable resistance that depends on factors such as temperature, the direction of current, or the applied voltage. For example, semiconductors like diodes or light bulbs show non-ohmic behavior. A diode, for instance, has a very small current when the voltage is below a certain threshold (reverse or forward bias), but once the threshold is exceeded, the current increases exponentially with voltage, which results in a nonlinear \( V \)-\( I \) characteristic. The graph of voltage vs current for a non-ohmic resistor is not a straight line but a curve, reflecting that the resistance is changing as voltage and current vary. Other examples of non-ohmic resistances include light bulbs, where the filament's resistance increases as the temperature rises due to an increase in current. Dynamic Resistance:
Dynamic resistance, also called incremental resistance, is the resistance of a non-ohmic component at a particular point on its current-voltage curve. It is defined as the ratio of the change in voltage (\( \Delta V \)) to the change in current (\( \Delta I \)) for small variations around a particular operating point on the curve. Mathematically, dynamic resistance is expressed as: \[ r_d = \frac{\Delta V}{\Delta I} \] This expression allows us to find the resistance at a specific point on the curve where the voltage and current are not constant. For instance, in a diode, the dynamic resistance changes depending on the voltage and current applied. At very small voltages (below the threshold), the dynamic resistance is very high, but after the threshold voltage is surpassed, the resistance drops significantly, and current increases more rapidly. Dynamic resistance is particularly useful for analyzing devices where the current-voltage relationship is nonlinear, such as in diodes or transistors. In contrast to static resistance, which is a fixed value in ohmic materials, dynamic resistance provides an instantaneous measure of how the component behaves under varying conditions.