Formulae
The rule that states that the current (I) flowing through a resistor (R) is directly proportional to the voltage (V) across the resistor, provided the temperature remains constant. is one of the most important laws of electrical circuits. It states that the current passing through a conductive material, eg a resistor, is equal to voltage divided by resistance. Ohm’s triangle can be used to remember three important equations:
- voltage (V) - the potential difference between two points, measured in volts (V)
- current (I) - the flow of electricity around a circuit, measured in amps (A)
- resistance (R) - how easily electricity flows through a wire, measured in ohms (Ω)
Resistors in series
Sometimes more than one resistor is used in a circuit. To calculate the combined resistance, each resistor’s value should be added together:
Resistance or Rtotal = R1 + R2 + R3
Example
What is the total value of resistors below?
Rtotal = R1 + R2 + R3
= 10 + 22 + 2,200
= 2,232 Ω
Question
What is the total value of resistors below?
Rtotal = R1 + R2 + R3
= 24 + 31 + 1500
= 1,555 Ω
Resistors in parallel
When resistors are placed in a parallel arrangement, the resistors are In a parallel circuit, the current divides into two or more paths before recombining to complete the circuit. Lamps and other components in these different paths are said to be in parallel. - the current is shared between each junction.
Resistance or 1/Rtotal = 1/R1 + 1/R2 + 1/R3
Example
What is the total resistance for the circuit below?
1/Rtotal = 1/R1 + 1/R2 + 1/R3
= 1/6 + 1/3 + 1/9
Give them a common denominator:
= 3/18 + 6/18 + 2/18
1/Rtotal = 11/18
Therefore, 11Rtotal = 18
Rtotal = 18/11
= 1.64 Ω
Question
What is the total resistance for the circuit below?
1/Rtotal = 1/R1 + 1/R2 + 1/R3
= 1/8 + 1/24 + 1/4
Common denominator:
= 3/24 + 1/24 + 6/24
1/Rtotal = 10/24
Therefore, 10Rtotaltotal = 24
Rtotal = 24/10
= 2.4 Ω
