Maths for Systems & Control
Ohm’s Law
- V: voltage, Volts (V)
- I: current, Amps (A)
- R: resistance, Ohms (Ω)
Example
An LED can take a maximum of 3V and has a safe current of up to 20mA. If the circuit was powered by a 6V battery, what size resistor would be needed to protect it?
As we have 6V in a circuit but an LED can only take 3V, we need to remove 3V from the circuit to prevent circuit failure. So:
So we would need a 150Ω resistor to prevent the LED from failing.
Electrical Power
- P: power, Watts (W)
- V: voltage, Volts (V)
- I: current, Amps (A)
Example
For the example above, would a 0.25W resistor be adequate?
The resistor would have to dissipate:
As a 0.25W resistor can dissipate up to 0.25W, this would be adequate for the LED.
Resistors in Series and Parallel
Resistors in Series
- Rt: total resistance, Ohms (Ω)
- R1: resistor 1, Ohms (Ω)
- R2: resistor 2, Ohms (Ω)
Resistors in Parallel
- Rt: total resistance, Ohms (Ω)
- R1: resistor 1, Ohms (Ω)
- R2: resistor 2, Ohms (Ω)
Potential Divider
For this circuit:
