Resistors in parallel circuits
When resistors are connected in parallel, we can calculate the total parallel resistance (RT) using the relationship;
\(\frac{1}{{{R_T}}} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}} + \frac{1}{{{R_3}}}\)
Let's use the same three resistance values as the previous example and calculate the total resistance when the resistors are connected in A type of circuit. A parallel circuit has more than one path for current..
The total resistance RT is found using the relationship;
\(\frac{1}{{{R_T}}} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}} + \frac{1}{{{R_3}}}\)
\(\frac{1}{{{R_T}}} = \frac{1}{{10}} + \frac{1}{{20}} + \frac{1}{{10}}\)
\(\frac{1}{{{R_T}}} = \frac{5}{{20}}\)
\(\frac{{{R_T}}}{1} = \frac{{20}}{5}\)
\({R_T} = 4\)
Total resistance is \(4\Omega\)
Hint 1
In parallel, the total resistance is always smaller than the smallest value resistor.
Hint 2
When completing the above calculation try using the fraction buttons on your calculator. If you don't have a fraction button, turn the fractions into decimals, eg;
\(\frac{1}{{20}} = 1 \div 20 = 0.05\)
Question
Calculate the total resistance RT in the following circuit.
\(\frac{1}{{{R_T}}} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}} + \frac{1}{{{R_3}}}\)
\(\frac{1}{{{R_T}}} = \frac{1}{{60}} + \frac{1}{{20}} + \frac{1}{{30}}\)
\(\frac{1}{{{R_T}}} = \frac{6}{{60}}\)
\(\frac{{{R_T}}}{1} = \frac{{60}}{6}\)
\({R_T} = 10\Omega\)
