Question

What is the equivalent resistance of the

following two resistors in parallel?
R₁
www
200 Ωپیشهl
250 Ω
Req =

Answer 1

Approximately
`111\; {\rm \Omega}`.

Step-by-step explanation:

It is given that
`R_(1) = 200\; {\Omega}` and
`R_(2) = 250\; {\Omega}` are connected in a circuit in parallel.

Assume that this circuit is powered with a direct current power supply of voltage
`V`.

Since
`R_(1)` and
`R_(2)` are connected in parallel, the voltage across the two resistors would both be
`V`. Thus, the current going through the two resistors would be
`(V / R_(1))` and
`(V / R_(2))`, respectively.

Also because the two resistors are connected in parallel, the total current in this circuit would be the sum of the current in each resistor:
`I = (V / R_(1)) + (V / R_(2))`.

In other words, if the voltage across this circuit is
`V`, the total current in this circuit would be
`I = (V / R_(1)) + (V / R_(2))`. The (equivalent) resistance
`R` of this circuit would be:

`\begin{aligned} R &= (V)/(I) \\ &= (V)/((V / R_(1)) + (V / R_(2))) \\ &= (1)/((1/R_(1)) + (1 / R_(2)))\end{aligned}`.

Given that
`R_(1) = 200\; {\Omega}` and
`R_(2) = 250\; {\Omega}`:

`\begin{aligned} R &= (1)/((1/R_(1)) + (1 / R_(2))) \\ &= \frac{1}{(1/(200\: {\rm \Omega})) + (1/(250\; {\rm \Omega}))} \\ &\approx 111\; {\rm \Omega}\end{aligned}`.