Physics 11

6.3 – Kirchhoff’s Laws

Learning Intentions:

I can:

✓ Calculate the total resistance of resistors connected in series ✓ Calculate equivalent resistance of a parallel network of resistors ✓ Solve problems with circuits series-parallel circuits

Series vs. Parallel

When designing an electric circuit, you can choose to connect things in a _________________ line one after another or to have a line ____________ in __________ or more directions. Take a resistor for example, if you connect four resistors in a _________________ line all along the same wire, we say that the resistors are connected in _______________. If you, instead, _____________ the wire into two directions and connect two resistors on each of the two lines, you we say that the resistors are connected in _________________. The way that things are connected in a circuit affects how they behave in the circuit.

Resistors in Series

If you connect resistors in a circuit in series, the ______________ resistance that they contribute to the circuit is _________________. That is, the total resistance is equal to the sum of the resistance of each resistor:

𝑅𝑠𝑒𝑟𝑖𝑒𝑠 = ∑𝑅𝑖

or

Using Ohm’s Law: 𝑉 = 𝐼𝑅

so

Where 𝑉𝑖 refers to the voltage across each resistor.

**Cells connected in series also behave like this. Note that the current is ______________ across the entire circuit**

Physics 11

Example:

Calculate the total resistance for a 650 ohm, a 350 ohm, and a 1000 ohm resistor connected in series.

On your Own:

Calculate the total resistance for ten 120 ohm resistors in series.

On your Own:

Francesca decorates her Christmas tree by connecting a string of fifty 15 ohm Christmas tree lights in series. Calculate the total resistance:

Resistors connected in Parallel

When resistors are connected in _________________ the current is _____________ into each of the branches and sent to each resistor separately. As a result, the total current _________________ the branches at the junction equals the total current _________________ the branches at the junction.

For example, consider three resistors connected in parallel:

The _______________ across the resistors in the three branches is equal to the _______________ voltage. The ________________ in each branch, however, is _________ equal. This is because current is related to the resistance of the circuit (𝐼 = 𝑉

𝑅).

Physics 11

Since each resistor is experiencing a _________________ current we cannot simply _________ them together to find the “total resistance” of the circuit. Instead, we use the following relationship to find the “_________________ _________________” of the parallel network:

1𝑅𝑃𝑎𝑟𝑎𝑙𝑙𝑒𝑙

= ∑1𝑅𝑖

or

Where 𝑅𝑃 represents the equivalent resistance for the parallel network of resistors.

Example:

Calculate the total resistance for two 180 ohm resistors connected in parallel.

Example:

A 10 ohm, 20 ohm, and 100 ohm resistors are connected in parallel. Calculate the total resistance.

Example:

Shawna decorates her Christmas tree by connecting a string of fifty 15 ohm Christmas tree lights in parallel. Calculate the total resistance.

Physics 11

Circuits with Series and Parallel

Some circuits have resistors connected in _____________ series and parallel. When solving these problems, calculate the _________________ resistance of each _________________ network then treat it as a ______________ resistor in _______________:

Example:

Two 33 ohm resistors are connected in parallel followed by two more 33 ohm resistors connected in parallel. What value of a single resistor would be used to replace these four resistors? Example: Two 15 ohm resistors are connected in series followed by 5 ohm, 3 ohm, and 12 ohm resistors connected in parallel. What is the total resistance across the circuit?

Kirchhoff’s Laws for Electric Circuits

The examples we have covered are applications of Kirchhoff’s laws for simple circuits. More complicated circuits can be solved using the ________________ form of Kirchhoff’s Laws:

Kirchhoff’s Current Rule:

At any junction in a circuit, the sum of all the currents entering that junction equals the sum of all currents leaving that junction.

Kirchhoff’s Voltage Rule:

The algebraic sum of all the changes in potential around a closed path in a circuit is zero.

Physics 11

Example:

Consider the following circuit. If there is a 100V potential difference across the terminals of the battery:

a) What is the equivalent resistance in the circuit?

b) Find the current in the circuit using Ohm’s Law

c) What is the voltage across the parallel network

Assignment: Worksheet P.251 # 1 ,2, 4,6-9