- Resistance: Resistance can be defined as the characteristic of a medium that opposes flow of current through itself. The unit of resistance is ohms which is represented by the Greek letter Ω (Omega) . The power value associated with resistance is quantified as the amount of power that the resistor can dissipate as heat without overheating itself.
The current (I) through the resistor (R) is defined as:
For a 1 Megaohm resistance, the current resulting from the application of 10 Volts would be 10 microamperes.
Figure 1. Simple Representation of Ohm's Law
Ohm’s law is the fundamental equation that describes the above relationship between the voltage potential, the current flowing in the circuit, and the resistance of a circuit. The power dissipated in a load resistance (R) is defined as the product of the current and the voltage. Other relationships for power can be easily derived from this by applying Ohm’s law using substitution.
The power (P) dissipated in (R) is defined as:
To calculate the value of resistance that will result in 10 Watts with 10 Volts applied to it, we remember that P = V2/R. Transposing, R = V2/P. The resistance is 100/10, or 10 ohms. So 10V applied to 10 ohms will yield 10 Watts. Any time two of the parameters (V, R, or P) are numerically the same, the third one will be the same. A common way to measure resistance is by using a Digital Multimeter (DMM).
Note:The power dissipation (P) is what sets the limit for how much voltage can be applied to the 50 ohm input of a digitizer. From the equations, we see that 10 Volts into 50 ohms will require the digitizer’s input load to dissipate 2 Watts. If you are running 2 channels, that’s 4 Watts. This amount of power dissipation is definitely something that can’t be ignored. Also notice that because of the square law effect, if you double that voltage into the digitizer, the power it must dissipate will QUADRUPLE.
Voltage Divider Calculation:
When two resistors are connected in a series configuration, they must share the applied voltage and the same current flows through both of them.
Figure 2. Voltage Divider Circuit Example
The formula used to calculate the applied voltage is:
(E1 = Voltage drop across R1)
(E2 = Voltage drop across R2)
To calculate the voltage across R2:
Note: Voltage divider is described by the equation above.
Current Divider Calculation:
When two resistors are connected in parallel configuration, the same voltage is across each of them. The amount of current flowing through them depends on the value of the resistances.
Figure 3. Current Divider Circuit Example
The above figure depicts two resistors in a parallel configuration.
Note: Digital multimeters (DMMs) are the most common measurement devices found in automated test systems. DMMs are usually simple to use and are often low-cost instruments. Generally, DMMs have built-in conditioning that provides:
a) High resolution (commonly measured in digits)
b) Multiple measurements (volts, current, resistance, etc)
c) Isolation and high voltage capabilities.