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

Total Resistance =
`(1300)/(9)` Ω (or 144.44 Ω)

Explanation:

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

`(1)/(Total)=(1)/(x)+(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:

`(1)/(Total)=(1)/(x)+(1)/(y)\\(1)/(Total)=(1)/(100)+(1)/(80)\\(1)/(Total)=(9)/(400)\\Total = (400)/(9)`

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

Total Resistance of Circuit =
`(400)/(9)+100=(1300)/(9)`

This is the total resistance of the circuit.