Question

Judge the equivalent resistance when the following are connected in parallel, 1 Ω and 10³Ω and 10⁶Ω.

Answer 1

Step 1 : Given data:

$R_1=1\Omega ,R_2={10}^3\Omega ,R_3={10}^6\Omega .$

Step 2 : Calculating equivalent resistance

The equivalent resistance in case of parallel combination is

$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$………$\left(1\right)$

Putting the values in $\left(1\right)$, we get

$$\begin{gathered} \frac{1}{R}=\frac{1}{1}+\frac{1}{{10}^3}+\frac{1}{{10}^6}=\frac{{10}^6+{10}^3+1}{{10}^6}=\frac{1001001}{1000000} \\ R=\frac{1000000}{1001001}=0.999\Omega \end{gathered}$$

Hence the equivalent resistance will be $0.999\Omega$