I-V curve

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An I/V curve (current voltage curve) is simply a Cartesian plot of the voltage across a resistor plotted against the current flowing through that resistor. Typically, voltage is plotted on the x-axis and current on the y-axis. An I/V curve is really nothing more than a plot of the equation V=IR (Ohm's Law) where V=voltage, I=current and R=resistance.

While I/V curves are applicable to any electrical system, they find wide use in the field of the study of biological electricity, particularly in the sub-field of electrophysiology. In this case, the voltage refers to the voltage across a biological membrane, or membrane potential, and the current is the flow of charged ions across channels in this membrane. The resistance is determined by the conductances of these channels.

Figure 1A sample "I/V curve showing its basic characteristics. It is a Cartesian coordinate system, essentially showing the relationship between current, voltage and resistance, (V=IR; Ohm's Law). Voltage (x-axis) is plotted against current (y-axis). The slope of the relationship gives the value of conductance (conductance = 1/resistance). For example, the brown line has a slope of 1, meaning it describes the current-voltage relationship of a 1 ohm resistor. The blue line has a slope of 0.5, or 2 ohms. Both the brown and blue lines illustrate the behavior of linear resistors (i.e. those that don't change resistance with voltage or current). The red line illustrates a rectifying resistor. That is, it passes current better in one direction than the other. With negative current values it has a resistance of 4 ohms, but at positive current values, its resistance is 10 ohms.
Figure 1A sample "I/V curve showing its basic characteristics. It is a Cartesian coordinate system, essentially showing the relationship between current, voltage and resistance, (V=IR; Ohm's Law). Voltage (x-axis) is plotted against current (y-axis). The slope of the relationship gives the value of conductance (conductance = 1/resistance). For example, the brown line has a slope of 1, meaning it describes the current-voltage relationship of a 1 ohm resistor. The blue line has a slope of 0.5, or 2 ohms. Both the brown and blue lines illustrate the behavior of linear resistors (i.e. those that don't change resistance with voltage or current). The red line illustrates a rectifying resistor. That is, it passes current better in one direction than the other. With negative current values it has a resistance of 4 ohms, but at positive current values, its resistance is 10 ohms.

In the case of ionic current flow across biological membranes, currents with a negative value are referred to as "inward current" while those with a positive value are known as "outward current".

An inward current is the result of positively charged ions crossing a cell membrane from the outside to the inside, or a negatively charged ion crossing from inside to outside.

An outward current is the result of positively charged ions crossing a cell membrane from the inside to the outside, or a negatively charged ion crossing from the outside to the inside.

In other words, the convention is that a current which increases positivity inside the cell is "inward" while a current that decreases positivity inside the cell is "outward".

Figure 2 Caption to be added
Figure 2 Caption to be added

Figure 2 shows an I/V curve that is more relevant to the current flows in excitable biological membranes (such as a neuronal axon). The blue line shows the I/V relationship for the potassium ion. Note that it is linear, indicating no voltage-dependent gating of the potassium ion channel. The yellow line shows the I/V relationship for the sodium ion. Note that it is not linear, indicating that the sodium ion channel is voltage-dependent. The green line indicates the I/V relationship derived from summing that of the sodium and potassium I/V's. This approximates the actual membrane potential and current relationship of a cell containing both types of channel.