Question

In a circuit, two resistors of 100 Ω and 80 Ω are connected in parallel. The parallel group is then connected in series with a 100 Ω resistor. What's the total resistance of the circuit?

Answer 1

Answer:

Total Resistance = $\frac{1300}{9}$ Ω  (or 144.44 Ω)

Step-by-step explanation:

If two resistors, with resistance x and y, are connected in parallel, their total resistance is given by the formula:

$\frac{1}{Total}=\frac{1}{x}+\frac{1}{y}$

If 2 resistors with resistance x and y and connected in series, their total resistance would be:

Total = x + y

Now, the first part, 100 and 80 are in parallel, so according to formula it would be:

$\frac{1}{Total}=\frac{1}{x}+\frac{1}{y}\\\frac{1}{Total}=\frac{1}{100}+\frac{1}{80}\\\frac{1}{Total}=\frac{9}{400}\\Total = \frac{400}{9}$

Now, this is connected in series with 100, so the grand total would be:

Total Resistance of Circuit = $\frac{400}{9}+100=\frac{1300}{9}$

This is the total resistance of the circuit.