**A basic circuit**

Here is an example of using Ohm’s Law for a basic circuit (see the electronics introduction if you’re not familiar with Ohm’s law.)

We have a resistor of 4k7 (4700 Ohm) connected to a 5V supply, what is the current flowing through it?

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**Answer**

I | = V/R |

= 5V/4k7 | |

= 1.06mA |

**Resistors in series**

When resistors are connected as shown in the example below, we say that they are connected in serial. Serial resistors have the following properties:

- The same current flow flows through them (Itotal = I1 = I2 = I3 ….)
- The total voltage will be a sum of the voltages across them (Vtotal = V1 + V2 + V3 …)
- The total resistance equals the sum of the individual resistors (Rtotal = R1 + R2 + R3 …)

**Example**A resistors of 10k is connected in series with a resistor of 4k7, what is the current through them and the voltage across each one individually?

**Answer**The voltage across both resistors is 5V, thus to calculate the current:

I | = V/R |

= 5V/(4k7 + 10k) | |

= 0.34mA |

The voltage over R1:

V1 | = I*R |

= 0.34mA*4k7 | |

= 1.6V |

The voltage over R2:

V2 | = I*R |

= 0.34mA*10k | |

= 3.4V |

And V1 + V2 = 5V!

**Resistors in Parallel**

When resistors are connected as shown in the example below, we say that they are connected in parallel. Resistors in parallel have the following properties:

- The voltage across them are the same (Vtotal = V1 = V2 =V3 …)
- The total current flowing through them will be the sum of the individual currents. (Itotal = I1 + I2 + I3 ….)
- The total resistance can be found by adding up the reciprocals of the resistors and then taking the reciprocal of the total (1/Rtotal = 1/R1+ 1/R2 + 1/R3 …)

There is an easy way to calculate the resistance of 2 resistors in parallel:

Rtotal = (R1 * R2) / (R1 + R2)

Here is the proof, for those interested:

1/Rt | = 1/R1 + 1/R2 |

1/Rt | = (R2 + R1) / (R1 * R2) |

1 | = ((R2 + R1) / (R1 * R2))*Rt |

(R1 * R2) / (R1 + R2) | = Rt |

**Example**

A resistors of 10k is connected in parallel with a resistor of 4k7, what is the current through them and the voltage across each one individually?

**Answer**

Because R1 and R2 are connected in parallel, the voltage over R1 equals the voltage over R2 namely 3.3V.

Let’s calculate the rest:

I1 | = V*R1 |

= 3.3V/4k7 | |

= 0.7mA |

I2 | = V*R2 |

= 3.3V/10k | |

= 0.33mA |

Rt | = (R1*R2)/(R1+R2) |

= 47k/14k7 | |

= 3k2 |

**Resistors as voltage dividers**

In many circuits you’ll see resistors used as voltage dividers. In the circuit below we have a 3.3V input voltage and want to calculate the voltage at point Vout. Because the resistors are in series, we know that the total voltage (3.3V in this example) will be divided between R1 and R2. A simple formula to calculate the potential (voltage) at point Vout is:

Vout = Vin * R2 / (R1+R2)

Here is the proof:

(1) | Itotal | = V1 / (R1 + R2) |

(2) | Vout | = Itotal * R2 |

Substituting (1) in (2): | ||

Vout | = (V1/ (R1 + R2)) * R2 | |

= V1 * R2 / (R1 + R2) | ||

= Vin * R2 / (R1 + R2) |

For the above circuit:

Vout | = Vin * R2 / (R1 + R2) |

= 3.3V * 10K / (10K + 4K7) | |

= 2.24V |