Given the parallel circuit above with the following values:

${ R }_{ 1 }=100\Omega \\ \\ { R }_{ 2 }=300\Omega \\ \\ { R }_{ 3 }=600\Omega \\ \\ { V }_{ T }=150V$

Find the total resistance ( ${ R }_{ T }$ ) of the circuit.

Give your answer to 2 decimal places.

The answer is 66.67.

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$\text{Resistance in a parallel connection is given by} \\ \frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}\\ \implies \frac{1}{R_p} = \frac{1}{100} + \frac{1}{300} + \frac{1}{600} \\ = \frac{1}{100} (\frac{1}{1} + \frac{1}{3} + \frac{1}{6}) = \frac{1}{100} ( frac{3}{2}) \\ \implies \frac{1}{R_p} = \frac{3}{200} \\ \implies R_p = \frac{200}{3} = 66.6666\\ \therefore \text{ The answer is } \fbox{66.67}$