Question

Judge the equivalent resistance when the following are connected in parallel - (a) 1 $\Omega$ and ${10}^6\Omega$, (b) $1\Omega$ and ${10}^3\Omega$ and ${10}^6\Omega$.

Answer 1

Since $1\Omega$ and 106 $\Omega$ are connected in parallel

then the equivalent resistance R will be

$\frac{1}{R}=\frac{1}{1}+\frac{1}{{10}^6}$

$R=\frac{{10}^6}{{10}^6+1}$ ~ $\frac{{10}^6}{{10}^6}$

$R=1\Omega$

Equivalent resistance is $1\Omega$

(b) $1\Omega$ and $103\Omega$ and $160\Omega$ are in parallel

$\frac{1}{R}=\frac{1}{1}+\frac{1}{{10}^3}+\frac{1}{{10}^6}$

$\frac{1}{R}=\frac{{10}^6+{10}^3+1}{{10}^6}$

$\frac{1}{R}=\frac{1001001}{1000000}$

$R=0.999\Omega$

Therefore, equivalent resistance $=0.999\Omega$