Higher example calculation
Example
Calculate the total resistance of the network of resistors.
This circuit contains a \({5}\Omega\) resistor in series with two resistors, \({6}\Omega\) and \({4}\Omega\), which are in parallel.
Start by calculating the combined resistance of the two parallel resistors.
\(\frac{1}{R}=\frac{1}{R}_{1}+\frac{1}{R}_{2}\)
R1 = \({6}\Omega\)
R2 = \({4}\Omega\)
\(\frac{1}{R}=\frac{1}{6} + \frac{1}{4}\)
\(\frac{1}{R}=\frac{5}{12}\)
R = \(\frac{12}{5}\)
R = \({2.4}\Omega\)
The network has been simplified to:
Now calculate the total resistance of the two resistors in series:
R = R1 + R 2
R = \({5}\Omega + {2.4}\Omega\)
R = \({7.4}\Omega\)
The total resistance of the network is \({7.4}\Omega\).
Example: Calculate total resistance
Calculate the total resistance of the network.
Answer
The two \({4}\Omega\) resistors are in parallel with each other.
The two \({10}\Omega\) resistors are in parallel with each other.
The two parallel networks are in series with each other.
First, calculate the total resistance of each parallel network:
| \(\frac{1}{R}=\frac{1}{R}_{1} +\frac{1}{R}_{2}\) | \(\frac{1}{R}=\frac{1}{R}_{1} +\frac{1}{R}_{2}\) |
| R1 = \({4}\Omega\) | R1 = \({10}\Omega\) |
| R2 = \({4}\Omega\) | R2 = \({10}\Omega\) |
| \(\frac{1}{R}=\frac{1}{4} +\frac{1}{4}\) | \(\frac{1}{R}=\frac{1}{10} +\frac{1}{10}\) |
| \(\frac{1}{R}=\frac{2}{4}\) | \(\frac{1}{R}=\frac{2}{10}\) |
| R = \(\frac{4}{2}\) | R = \(\frac{10}{2}\) |
| R = \({2}\Omega\) | R = \({5}\Omega\) |
| \(\frac{1}{R}=\frac{1}{R}_{1} +\frac{1}{R}_{2}\) |
| \(\frac{1}{R}=\frac{1}{R}_{1} +\frac{1}{R}_{2}\) |
| R1 = \({4}\Omega\) |
| R1 = \({10}\Omega\) |
| R2 = \({4}\Omega\) |
| R2 = \({10}\Omega\) |
| \(\frac{1}{R}=\frac{1}{4} +\frac{1}{4}\) |
| \(\frac{1}{R}=\frac{1}{10} +\frac{1}{10}\) |
| \(\frac{1}{R}=\frac{2}{4}\) |
| \(\frac{1}{R}=\frac{2}{10}\) |
| R = \(\frac{4}{2}\) |
| R = \(\frac{10}{2}\) |
| R = \({2}\Omega\) |
| R = \({5}\Omega\) |
The network has been simplified to:
Now calculate the total resistance of the two resistors in series.
R = R1 + R2
R = \({2}\Omega + {5}\Omega\)
R = \({7}\Omega\)
The total resistance of the network is \({7}\Omega\).
