# Voltage Coefficient of Resistance

on . Posted in Electrical Engineering

Voltage coefficient of resistance, abbreviated as VCR, is a measure of how the electrical resistance of a material changes with variations in voltage.  It quantifies the percentage change in resistance per unit change in voltage.  Typically, VCR is expressed as a fractional change in resistance per unit change in voltage.  For example, if VCR is 0.001 per volt (0.001/V), it means that for every 1-volt change in applied voltage, the resistance of the material changes by 0.001 times its initial value.

Understanding the voltage coefficient of resistance is crucial in various electronic and electrical applications.  It helps engineers and designers account for changes in resistance when designing circuits or selecting materials for specific applications.  Materials with stable or low VCR are often preferred for applications where precise resistance values are critical, such as in precision resistors and temperature sensors.

### Materials can have positive or negative VCR

• Positive VCR  -  When the resistance of a material increases with an increase in voltage, it has a positive VCR.  This behavior is typical in materials like semiconductors and some conductive polymers.
• Negative VCR  -  When the resistance of a material decreases with an increase in voltage, it has a negative VCR.  Materials with negative VCR are less common but can be found in some specialized applications.

### Voltage Coefficient of Resistance formula

$$VCR = 100 \; ( R_1 \;-\; R_2 ) \;/\; R_2 \; ( V_1 \;-\; V_2 )$$
Symbol English Metric
$$VCR$$ = voltage coefficient of resistance $$\Omega$$ $$kg-m^2 \;/\; s^3-A^2$$
$$R_1$$ = resistance at the rated voltage $$V_1$$ $$\Omega$$ $$kg-m^2 \;/\; s^3-A^2$$
$$R_2$$ = resistance at 10% of rated voltage $$V_2$$ $$\Omega$$ $$kg-m^2 \;/\; s^3-A^2$$