Question

What is the equivalent resistance of the

Answer 1

Answer:

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

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:

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

Given that $R_{1} = 200\; {\Omega}$ and $R_{2} = 250\; {\Omega}$:

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